Apostila de calculo IV 1990

99
\JE'OfUfltL Q..u.7\N'Q. ... c" 0.0 de J .. - "'\ li) ;: "1f.l t) l + ou de j

description

Apostila de calculo IV 1990

Transcript of Apostila de calculo IV 1990

Page 1: Apostila de calculo  IV  1990

ccedil~A~Nleuro~~Cj~tI~Kt~ CcedilotOacuteeurol~ JEOfUfltL ~ Qu7NQ c 00I)h~~ ~~J)QNQ de ~eNINampQ J

I)~ ~ ~~ ~ - li) 1flt) l ~ ~ l~0 + YCt-y~

ou f~~ de -n~~Y~lt7Qi)

oacute~J~---V j

_ (J) ~1urmi ia~ l i-7iti6v) ~J_r6Uoo_do + ~ r Q - fi - 5 ~ I VO cli ~ o 3[ + ~1- se

Lo~t~ ~~ eoMJi~oo ~O-) e loL+ tkr ~ lltll+4Jj 4- lltY +tb3)lt ~li-) ~ l tt-t 3l lr + t-3 1--~)J + ( 6 - 3-t-) k ~OTA- 1 Q l-06 i +ltgteacuteJ) __ ~ ~~~~ ~ ~ ~ ~ 4e k~~+-

iItd4 Jwk ~ ck ~ de ~~

~ Cl----Pj

~ t01 Utl~) B ( b b~ hJ

~ l) ~ ~Qi lloi-o) t lt + lQgt~ l t~- Q)11-t ~Q~~(b3-1J3hJ ~

reg ~t) IrNfNl o ~qii agraveA ~ ~-ck t Agrave l 2gt t al B l-f G3)

-e~ ltxl)~ l31--1l- )+ (1+5t)J -4 (l+it)k -lO-rA 1 euro l- cd cb )

1) -t~ (ew~) F1

t Q A

t~ a ~1 C

t-~ -o

t a] A

i~

1-+1shyl

Q bshy

~ ~-l ~ b~ ~

) (DI)lt- -t IJv-lt t

4 = i

~ lrL Q COO 1 ~ J)UA1 e 0 ~ltwJ

-l-) Q ~fll 1 ~ 4 ~1-S + c -lt lt-10

------

c~ ~l+L ~L- i+ jl-)r+ amp-(1-) ~

e ~clA CoIYYlO

~ Fl ~j ~ ~lt-=0

e(~Ij~-O

i~QNNlO QJ(t (b) ~~t ~u1~-lLt jmiddotCcedilOraquo) 1r ~~ ~

~ t1) t---t=-f_-=-(ij-=-r~+~-(f_~-)~~=l

~ltl-)~ ti t~Z J+t~ t~ (-~) 00)

~ )ecirc~f~ i l~Q-- ~~ ~-~

(-= O

~~t I ~ i~ I O

~~ tl)~ l- M1S~ te [-ii1

reg ) ~~ otildej-- ir 2~

l ~ ~J 1 agrave-=-

-----

j 1oQovdo ~ Ccedilu--J

) ~~ 1- =gt~- 2- = f

L-agrave1- + bt t-3~ l~L ~ - 3J-=-6

-~= - 8 -~

~ ~~

~L+ ~11 Cb-td = o

)

j = ~1-4 l tti)2

-= o

-0lt39 ~ t~ ~-J e 7 t o axl) + 4-t ++1) j cr

~W O d~o k llt ~~_~ lhi)1gt

4-4ll--t-)2 =70

i_ l +)lO

Lr J o ~ - ~-+ 2t+Aacute7 oO

te t-zo] - H l-z)~t

) ~ l((+l+ 1~1

l =o

~ I

ll~tr ~~t J

~ ~~1 1

C-Io~ t-

L l= ~~t-

nU)= l CiacuteD~l- i) L -- ~J)eM t r t E to ert J

jl~ ~ ~lL i ~+)Q )2Ntl ~ i ~+

i ~ coocirc1 i 2 ltA41 iL

~ ~L1 (lJMt -1) t(oIJ - r-r te tOltl(]

(- tmccedil~~ J~~~ ~~~ ~ ~ olo~ ~ bull ~ lt~~ d-t~ ~~~

~COlPRMENTO DE f1RCO ~

~Ic

st~MOI a ew_ c JoJc it L) t e t o 1 Co ~ L-) ltoMl-shy~~ ampN~ QMA (0 ~1

i~ltA ut a ~~ Q shy

~CV~ ) dQJYVO tM~ le 4UJl Q- ClMItQ

1 eacute C~ ~fIM ~~

~

~ ~~ _ Q AeMl -c -+ o COotildetj

~ ~ dl

(_ oIAAeMrt -c Q CltJ1--n (-Cl J)ltlM 4c o Cogt ~J )= o~++03~t= ~l~+tCltJt)ci 211 ~tl lii(1bull jl bull Jo liotildeP d 1o dl bull o ~t 10 middot bulllIo

~bealY() nulYlO c~Qwo o = -OiD ~ )lt ~llo ltgtJ1i~

b

-Ae CIXJV~ VfIJ)oacute o ~ ~ t ) twa~ ~iOO (oh fgtAgrave ~1 tvM ~ltOJJ Q 0 OAA o Ij

~=~ l~cvJ)

o1lTir~ decirc OICO fj= l Q dL o J Jt-j I)~ Q t

~ ~~~Oo reg r~1 ~ clD ~ nrF do= ~di li 5dJJ = j V1 ~ ~

4 J~tt

---_ ~~-

- -1

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 2: Apostila de calculo  IV  1990

_ (J) ~1urmi ia~ l i-7iti6v) ~J_r6Uoo_do + ~ r Q - fi - 5 ~ I VO cli ~ o 3[ + ~1- se

Lo~t~ ~~ eoMJi~oo ~O-) e loL+ tkr ~ lltll+4Jj 4- lltY +tb3)lt ~li-) ~ l tt-t 3l lr + t-3 1--~)J + ( 6 - 3-t-) k ~OTA- 1 Q l-06 i +ltgteacuteJ) __ ~ ~~~~ ~ ~ ~ ~ 4e k~~+-

iItd4 Jwk ~ ck ~ de ~~

~ Cl----Pj

~ t01 Utl~) B ( b b~ hJ

~ l) ~ ~Qi lloi-o) t lt + lQgt~ l t~- Q)11-t ~Q~~(b3-1J3hJ ~

reg ~t) IrNfNl o ~qii agraveA ~ ~-ck t Agrave l 2gt t al B l-f G3)

-e~ ltxl)~ l31--1l- )+ (1+5t)J -4 (l+it)k -lO-rA 1 euro l- cd cb )

1) -t~ (ew~) F1

t Q A

t~ a ~1 C

t-~ -o

t a] A

i~

1-+1shyl

Q bshy

~ ~-l ~ b~ ~

) (DI)lt- -t IJv-lt t

4 = i

~ lrL Q COO 1 ~ J)UA1 e 0 ~ltwJ

-l-) Q ~fll 1 ~ 4 ~1-S + c -lt lt-10

------

c~ ~l+L ~L- i+ jl-)r+ amp-(1-) ~

e ~clA CoIYYlO

~ Fl ~j ~ ~lt-=0

e(~Ij~-O

i~QNNlO QJ(t (b) ~~t ~u1~-lLt jmiddotCcedilOraquo) 1r ~~ ~

~ t1) t---t=-f_-=-(ij-=-r~+~-(f_~-)~~=l

~ltl-)~ ti t~Z J+t~ t~ (-~) 00)

~ )ecirc~f~ i l~Q-- ~~ ~-~

(-= O

~~t I ~ i~ I O

~~ tl)~ l- M1S~ te [-ii1

reg ) ~~ otildej-- ir 2~

l ~ ~J 1 agrave-=-

-----

j 1oQovdo ~ Ccedilu--J

) ~~ 1- =gt~- 2- = f

L-agrave1- + bt t-3~ l~L ~ - 3J-=-6

-~= - 8 -~

~ ~~

~L+ ~11 Cb-td = o

)

j = ~1-4 l tti)2

-= o

-0lt39 ~ t~ ~-J e 7 t o axl) + 4-t ++1) j cr

~W O d~o k llt ~~_~ lhi)1gt

4-4ll--t-)2 =70

i_ l +)lO

Lr J o ~ - ~-+ 2t+Aacute7 oO

te t-zo] - H l-z)~t

) ~ l((+l+ 1~1

l =o

~ I

ll~tr ~~t J

~ ~~1 1

C-Io~ t-

L l= ~~t-

nU)= l CiacuteD~l- i) L -- ~J)eM t r t E to ert J

jl~ ~ ~lL i ~+)Q )2Ntl ~ i ~+

i ~ coocirc1 i 2 ltA41 iL

~ ~L1 (lJMt -1) t(oIJ - r-r te tOltl(]

(- tmccedil~~ J~~~ ~~~ ~ ~ olo~ ~ bull ~ lt~~ d-t~ ~~~

~COlPRMENTO DE f1RCO ~

~Ic

st~MOI a ew_ c JoJc it L) t e t o 1 Co ~ L-) ltoMl-shy~~ ampN~ QMA (0 ~1

i~ltA ut a ~~ Q shy

~CV~ ) dQJYVO tM~ le 4UJl Q- ClMItQ

1 eacute C~ ~fIM ~~

~

~ ~~ _ Q AeMl -c -+ o COotildetj

~ ~ dl

(_ oIAAeMrt -c Q CltJ1--n (-Cl J)ltlM 4c o Cogt ~J )= o~++03~t= ~l~+tCltJt)ci 211 ~tl lii(1bull jl bull Jo liotildeP d 1o dl bull o ~t 10 middot bulllIo

~bealY() nulYlO c~Qwo o = -OiD ~ )lt ~llo ltgtJ1i~

b

-Ae CIXJV~ VfIJ)oacute o ~ ~ t ) twa~ ~iOO (oh fgtAgrave ~1 tvM ~ltOJJ Q 0 OAA o Ij

~=~ l~cvJ)

o1lTir~ decirc OICO fj= l Q dL o J Jt-j I)~ Q t

~ ~~~Oo reg r~1 ~ clD ~ nrF do= ~di li 5dJJ = j V1 ~ ~

4 J~tt

---_ ~~-

- -1

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 3: Apostila de calculo  IV  1990

i~

1-+1shyl

Q bshy

~ ~-l ~ b~ ~

) (DI)lt- -t IJv-lt t

4 = i

~ lrL Q COO 1 ~ J)UA1 e 0 ~ltwJ

-l-) Q ~fll 1 ~ 4 ~1-S + c -lt lt-10

------

c~ ~l+L ~L- i+ jl-)r+ amp-(1-) ~

e ~clA CoIYYlO

~ Fl ~j ~ ~lt-=0

e(~Ij~-O

i~QNNlO QJ(t (b) ~~t ~u1~-lLt jmiddotCcedilOraquo) 1r ~~ ~

~ t1) t---t=-f_-=-(ij-=-r~+~-(f_~-)~~=l

~ltl-)~ ti t~Z J+t~ t~ (-~) 00)

~ )ecirc~f~ i l~Q-- ~~ ~-~

(-= O

~~t I ~ i~ I O

~~ tl)~ l- M1S~ te [-ii1

reg ) ~~ otildej-- ir 2~

l ~ ~J 1 agrave-=-

-----

j 1oQovdo ~ Ccedilu--J

) ~~ 1- =gt~- 2- = f

L-agrave1- + bt t-3~ l~L ~ - 3J-=-6

-~= - 8 -~

~ ~~

~L+ ~11 Cb-td = o

)

j = ~1-4 l tti)2

-= o

-0lt39 ~ t~ ~-J e 7 t o axl) + 4-t ++1) j cr

~W O d~o k llt ~~_~ lhi)1gt

4-4ll--t-)2 =70

i_ l +)lO

Lr J o ~ - ~-+ 2t+Aacute7 oO

te t-zo] - H l-z)~t

) ~ l((+l+ 1~1

l =o

~ I

ll~tr ~~t J

~ ~~1 1

C-Io~ t-

L l= ~~t-

nU)= l CiacuteD~l- i) L -- ~J)eM t r t E to ert J

jl~ ~ ~lL i ~+)Q )2Ntl ~ i ~+

i ~ coocirc1 i 2 ltA41 iL

~ ~L1 (lJMt -1) t(oIJ - r-r te tOltl(]

(- tmccedil~~ J~~~ ~~~ ~ ~ olo~ ~ bull ~ lt~~ d-t~ ~~~

~COlPRMENTO DE f1RCO ~

~Ic

st~MOI a ew_ c JoJc it L) t e t o 1 Co ~ L-) ltoMl-shy~~ ampN~ QMA (0 ~1

i~ltA ut a ~~ Q shy

~CV~ ) dQJYVO tM~ le 4UJl Q- ClMItQ

1 eacute C~ ~fIM ~~

~

~ ~~ _ Q AeMl -c -+ o COotildetj

~ ~ dl

(_ oIAAeMrt -c Q CltJ1--n (-Cl J)ltlM 4c o Cogt ~J )= o~++03~t= ~l~+tCltJt)ci 211 ~tl lii(1bull jl bull Jo liotildeP d 1o dl bull o ~t 10 middot bulllIo

~bealY() nulYlO c~Qwo o = -OiD ~ )lt ~llo ltgtJ1i~

b

-Ae CIXJV~ VfIJ)oacute o ~ ~ t ) twa~ ~iOO (oh fgtAgrave ~1 tvM ~ltOJJ Q 0 OAA o Ij

~=~ l~cvJ)

o1lTir~ decirc OICO fj= l Q dL o J Jt-j I)~ Q t

~ ~~~Oo reg r~1 ~ clD ~ nrF do= ~di li 5dJJ = j V1 ~ ~

4 J~tt

---_ ~~-

- -1

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 4: Apostila de calculo  IV  1990

------

c~ ~l+L ~L- i+ jl-)r+ amp-(1-) ~

e ~clA CoIYYlO

~ Fl ~j ~ ~lt-=0

e(~Ij~-O

i~QNNlO QJ(t (b) ~~t ~u1~-lLt jmiddotCcedilOraquo) 1r ~~ ~

~ t1) t---t=-f_-=-(ij-=-r~+~-(f_~-)~~=l

~ltl-)~ ti t~Z J+t~ t~ (-~) 00)

~ )ecirc~f~ i l~Q-- ~~ ~-~

(-= O

~~t I ~ i~ I O

~~ tl)~ l- M1S~ te [-ii1

reg ) ~~ otildej-- ir 2~

l ~ ~J 1 agrave-=-

-----

j 1oQovdo ~ Ccedilu--J

) ~~ 1- =gt~- 2- = f

L-agrave1- + bt t-3~ l~L ~ - 3J-=-6

-~= - 8 -~

~ ~~

~L+ ~11 Cb-td = o

)

j = ~1-4 l tti)2

-= o

-0lt39 ~ t~ ~-J e 7 t o axl) + 4-t ++1) j cr

~W O d~o k llt ~~_~ lhi)1gt

4-4ll--t-)2 =70

i_ l +)lO

Lr J o ~ - ~-+ 2t+Aacute7 oO

te t-zo] - H l-z)~t

) ~ l((+l+ 1~1

l =o

~ I

ll~tr ~~t J

~ ~~1 1

C-Io~ t-

L l= ~~t-

nU)= l CiacuteD~l- i) L -- ~J)eM t r t E to ert J

jl~ ~ ~lL i ~+)Q )2Ntl ~ i ~+

i ~ coocirc1 i 2 ltA41 iL

~ ~L1 (lJMt -1) t(oIJ - r-r te tOltl(]

(- tmccedil~~ J~~~ ~~~ ~ ~ olo~ ~ bull ~ lt~~ d-t~ ~~~

~COlPRMENTO DE f1RCO ~

~Ic

st~MOI a ew_ c JoJc it L) t e t o 1 Co ~ L-) ltoMl-shy~~ ampN~ QMA (0 ~1

i~ltA ut a ~~ Q shy

~CV~ ) dQJYVO tM~ le 4UJl Q- ClMItQ

1 eacute C~ ~fIM ~~

~

~ ~~ _ Q AeMl -c -+ o COotildetj

~ ~ dl

(_ oIAAeMrt -c Q CltJ1--n (-Cl J)ltlM 4c o Cogt ~J )= o~++03~t= ~l~+tCltJt)ci 211 ~tl lii(1bull jl bull Jo liotildeP d 1o dl bull o ~t 10 middot bulllIo

~bealY() nulYlO c~Qwo o = -OiD ~ )lt ~llo ltgtJ1i~

b

-Ae CIXJV~ VfIJ)oacute o ~ ~ t ) twa~ ~iOO (oh fgtAgrave ~1 tvM ~ltOJJ Q 0 OAA o Ij

~=~ l~cvJ)

o1lTir~ decirc OICO fj= l Q dL o J Jt-j I)~ Q t

~ ~~~Oo reg r~1 ~ clD ~ nrF do= ~di li 5dJJ = j V1 ~ ~

4 J~tt

---_ ~~-

- -1

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 5: Apostila de calculo  IV  1990

-----

j 1oQovdo ~ Ccedilu--J

) ~~ 1- =gt~- 2- = f

L-agrave1- + bt t-3~ l~L ~ - 3J-=-6

-~= - 8 -~

~ ~~

~L+ ~11 Cb-td = o

)

j = ~1-4 l tti)2

-= o

-0lt39 ~ t~ ~-J e 7 t o axl) + 4-t ++1) j cr

~W O d~o k llt ~~_~ lhi)1gt

4-4ll--t-)2 =70

i_ l +)lO

Lr J o ~ - ~-+ 2t+Aacute7 oO

te t-zo] - H l-z)~t

) ~ l((+l+ 1~1

l =o

~ I

ll~tr ~~t J

~ ~~1 1

C-Io~ t-

L l= ~~t-

nU)= l CiacuteD~l- i) L -- ~J)eM t r t E to ert J

jl~ ~ ~lL i ~+)Q )2Ntl ~ i ~+

i ~ coocirc1 i 2 ltA41 iL

~ ~L1 (lJMt -1) t(oIJ - r-r te tOltl(]

(- tmccedil~~ J~~~ ~~~ ~ ~ olo~ ~ bull ~ lt~~ d-t~ ~~~

~COlPRMENTO DE f1RCO ~

~Ic

st~MOI a ew_ c JoJc it L) t e t o 1 Co ~ L-) ltoMl-shy~~ ampN~ QMA (0 ~1

i~ltA ut a ~~ Q shy

~CV~ ) dQJYVO tM~ le 4UJl Q- ClMItQ

1 eacute C~ ~fIM ~~

~

~ ~~ _ Q AeMl -c -+ o COotildetj

~ ~ dl

(_ oIAAeMrt -c Q CltJ1--n (-Cl J)ltlM 4c o Cogt ~J )= o~++03~t= ~l~+tCltJt)ci 211 ~tl lii(1bull jl bull Jo liotildeP d 1o dl bull o ~t 10 middot bulllIo

~bealY() nulYlO c~Qwo o = -OiD ~ )lt ~llo ltgtJ1i~

b

-Ae CIXJV~ VfIJ)oacute o ~ ~ t ) twa~ ~iOO (oh fgtAgrave ~1 tvM ~ltOJJ Q 0 OAA o Ij

~=~ l~cvJ)

o1lTir~ decirc OICO fj= l Q dL o J Jt-j I)~ Q t

~ ~~~Oo reg r~1 ~ clD ~ nrF do= ~di li 5dJJ = j V1 ~ ~

4 J~tt

---_ ~~-

- -1

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 6: Apostila de calculo  IV  1990

) ~ l((+l+ 1~1

l =o

~ I

ll~tr ~~t J

~ ~~1 1

C-Io~ t-

L l= ~~t-

nU)= l CiacuteD~l- i) L -- ~J)eM t r t E to ert J

jl~ ~ ~lL i ~+)Q )2Ntl ~ i ~+

i ~ coocirc1 i 2 ltA41 iL

~ ~L1 (lJMt -1) t(oIJ - r-r te tOltl(]

(- tmccedil~~ J~~~ ~~~ ~ ~ olo~ ~ bull ~ lt~~ d-t~ ~~~

~COlPRMENTO DE f1RCO ~

~Ic

st~MOI a ew_ c JoJc it L) t e t o 1 Co ~ L-) ltoMl-shy~~ ampN~ QMA (0 ~1

i~ltA ut a ~~ Q shy

~CV~ ) dQJYVO tM~ le 4UJl Q- ClMItQ

1 eacute C~ ~fIM ~~

~

~ ~~ _ Q AeMl -c -+ o COotildetj

~ ~ dl

(_ oIAAeMrt -c Q CltJ1--n (-Cl J)ltlM 4c o Cogt ~J )= o~++03~t= ~l~+tCltJt)ci 211 ~tl lii(1bull jl bull Jo liotildeP d 1o dl bull o ~t 10 middot bulllIo

~bealY() nulYlO c~Qwo o = -OiD ~ )lt ~llo ltgtJ1i~

b

-Ae CIXJV~ VfIJ)oacute o ~ ~ t ) twa~ ~iOO (oh fgtAgrave ~1 tvM ~ltOJJ Q 0 OAA o Ij

~=~ l~cvJ)

o1lTir~ decirc OICO fj= l Q dL o J Jt-j I)~ Q t

~ ~~~Oo reg r~1 ~ clD ~ nrF do= ~di li 5dJJ = j V1 ~ ~

4 J~tt

---_ ~~-

- -1

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 7: Apostila de calculo  IV  1990

~COlPRMENTO DE f1RCO ~

~Ic

st~MOI a ew_ c JoJc it L) t e t o 1 Co ~ L-) ltoMl-shy~~ ampN~ QMA (0 ~1

i~ltA ut a ~~ Q shy

~CV~ ) dQJYVO tM~ le 4UJl Q- ClMItQ

1 eacute C~ ~fIM ~~

~

~ ~~ _ Q AeMl -c -+ o COotildetj

~ ~ dl

(_ oIAAeMrt -c Q CltJ1--n (-Cl J)ltlM 4c o Cogt ~J )= o~++03~t= ~l~+tCltJt)ci 211 ~tl lii(1bull jl bull Jo liotildeP d 1o dl bull o ~t 10 middot bulllIo

~bealY() nulYlO c~Qwo o = -OiD ~ )lt ~llo ltgtJ1i~

b

-Ae CIXJV~ VfIJ)oacute o ~ ~ t ) twa~ ~iOO (oh fgtAgrave ~1 tvM ~ltOJJ Q 0 OAA o Ij

~=~ l~cvJ)

o1lTir~ decirc OICO fj= l Q dL o J Jt-j I)~ Q t

~ ~~~Oo reg r~1 ~ clD ~ nrF do= ~di li 5dJJ = j V1 ~ ~

4 J~tt

---_ ~~-

- -1

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 8: Apostila de calculo  IV  1990

~

~ ~~ _ Q AeMl -c -+ o COotildetj

~ ~ dl

(_ oIAAeMrt -c Q CltJ1--n (-Cl J)ltlM 4c o Cogt ~J )= o~++03~t= ~l~+tCltJt)ci 211 ~tl lii(1bull jl bull Jo liotildeP d 1o dl bull o ~t 10 middot bulllIo

~bealY() nulYlO c~Qwo o = -OiD ~ )lt ~llo ltgtJ1i~

b

-Ae CIXJV~ VfIJ)oacute o ~ ~ t ) twa~ ~iOO (oh fgtAgrave ~1 tvM ~ltOJJ Q 0 OAA o Ij

~=~ l~cvJ)

o1lTir~ decirc OICO fj= l Q dL o J Jt-j I)~ Q t

~ ~~~Oo reg r~1 ~ clD ~ nrF do= ~di li 5dJJ = j V1 ~ ~

4 J~tt

---_ ~~-

- -1

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 9: Apostila de calculo  IV  1990

- -1

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 10: Apostila de calculo  IV  1990

r e i eoiM~~ NO ~QC-euro amp ~oMao tti lt reg 1

~ 0= ~Iob~ti ~I)eacute o ~o cicx ~CQ

ocltt i ltIII~~ -- ~~ amp vfWilA

~-t ri w

lo

~ N t t) shy ~

___-w clf c~

w-krS ~A z eJ~ Q~ 3 ~3- Jo6c IMc tIacutet I

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 11: Apostila de calculo  IV  1990

_~~~------ ---~-~__-~

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 12: Apostila de calculo  IV  1990

bull

-

_~-------~

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 13: Apostila de calculo  IV  1990

)

~ _)0v ~ 7 lto Oacute 1)-0shya ~ j

bull

~~ shy 4~ do o ~-ltagraveC2 0-~Nchi-0 CI~

0) ~ lgtt) o ClJOS( L+ Q ~ 1+ c t k

b) ~ (1raquo) a cogt2 t + Q ~ ~_tf- Sj ~ w JJJ vJ

-P

~ - - Q tjQM- ~ + o Cob4 1 Q k

~ I ~ ~+ e~ w

+

uacute = o~ ~ ~ 02-+ e~

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 14: Apostila de calculo  IV  1990

iclt +shy

tJlt

1

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 15: Apostila de calculo  IV  1990

I bull I

I I bull I i

I bull I I

I I I I bullbull I 1 I

~ I ~II4tshy I 1 Q-to t ll ~middoti t-r ()t n

~

j I bull

I I

Dgt----~~ __ +- __ 1- I

I I I I j I I J I I I

~ I I I

~ ~ ~ t1l 1 ht

h~r ~( t~fJ - ~ ( tIt-d

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 16: Apostila de calculo  IV  1990

A c

~)-k fl~fl Q(06~ lt 0216+(1t-1) dagrave- 06=())~

3) JJt(tiaJ+~ (-liTI~1tt(11~1r2(t~~~

4)1 -I1(1 acirc-) d t~ ~) ~ JFie~ltI ) ddi --1~uacutet I -) c agrave-shy

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 17: Apostila de calculo  IV  1990

_---8

A

CAacutelCUlO _ ~ONI ~1J e ~ti~) lO 6~ ~ ~~ ~~1t1 ocirc-) middotn_l(b) )ltl ~t)J ~ f l~)

~tl~ ~) ~L(1tH 1lt) ~t)J Gumiddot) l e La bJ

~~---_ ~~~--~_

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 18: Apostila de calculo  IV  1990

-)

11 ~~

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 19: Apostila de calculo  IV  1990

r ~ Jgt CUAcirc~ ie~

~

~oo o -IIWllIW ~ F60 Cltl~ a otn dt ~inoJ

lyJeAOl (~~ltriacuteo NIuuml lt2D~) o- ~~JV(IUuml fR ~ lC1Ocirc) ~c+ ~ L l ~ 11 ll~j atilde-) d ou

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 20: Apostila de calculo  IV  1990

bull

-- shy

lJ(M1) oi ~J~ - ) llt-t VL + 1( bullbull) d~ lt

c~ ~

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 21: Apostila de calculo  IV  1990

~ IL03ltJ

~l~gt t~~~

~) (b]euk

A-B t i 6-= 3fz

~(i23)

oos

ecircJ= 3i~ 3

~ J t lb

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 22: Apostila de calculo  IV  1990

( shy

J~ -c

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 23: Apostila de calculo  IV  1990

I

Bbli lt-t )Q

( 0 d rJc +( J j ii jJ r(i 1 -)-~

~~tJ~ r ~ dj ~ J

~gc A~ middotE c (2()y ~~ doIJ ()Af(Aacute (0 cc J LI dc Cl-C0 ~3 ~) ~cs)~~d~ ~ ~i c~ ltti

~~~ ampA Cltgtlt(~~ de ohtO Uacuteo~~ tL~i-~ ol~~ e- -l~) ) ) ollj =1

---- --- -----_- ---- ~~

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 24: Apostila de calculo  IV  1990

I

t e(liacutef ~ d-ltl

reg c ltl ~Uyt jl-l J ~)~ te (~bJo

Ic +l~fl P d~ jn 1iacuteltl jllol I ~(lJ ] ~ d-1 o U-A ~ ~ k

~ l~ bull~ ) ai

reg Q ~(b) al)W1l~)rqt)t) oeuro t bgt~1 1c ~lII b-) d~ J41t [clotilde) j l~ll 1fIacute~)] 1lt1

7)0

d Qo1wlto + ltk C cL ~~

t doacute J1ft lt4 wJdt ~ R Cl~ l 5 (i-l-1I] gt a-fsl~ gtfwl

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 25: Apostila de calculo  IV  1990

~~ reg J rut~j as

c

cmiddotctiU)= 3~~~~k ~~t--r tamp ~ o ~~]

b) ~~ o QcrM~~ ltk C

9vd

()) j lJt~ ~ d o J~ (~- t-) ~ 2gti)Qov~ c o

-~ _ 3 1~ttt- 3 co ) tI -+ -4 ~l ~ ~ ~ 9 -m ~=3

agravet Li

f)11 1 ~ 9 enN 3))1 dAJ [ Il (3coot)lt BJQMt ] o dt o

o 2l = 6 21 Cob(t- I)ev dl

- 16lt

o

r~6~~-(~+) cli

-=--~ gtC ~

o

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 26: Apostila de calculo  IV  1990

~wk euro) j ruf~j as

c

eClt) 3 ~tlf1 k aMN -1 tG t Olt~]

~d

()) Jt(j J o Jlt (~CCgt -t ~ $ov~ c o

-~ _31~tt-+ 3c4)6t -+ ~ AJ=~l~9m ~3

d-t L1f

~11 1 ~ s ltOO~l qJl t JtJ[a (3Co1gtt)~middot ocirc~Wt JDtt o o Ll

-t62 J eabt llQv ltL-l

= - b~ o

1L6~~ - (lt~l Jl = ()

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 27: Apostila de calculo  IV  1990

bull

_ shy

Me~ )(ltf- J~+ t) clJ c

l (i) O O )

aliObi)

1[~t+~+ 3J JiWJ1 c

i I( sA)hN~lt o 70-tlii _~ -- ~~l +3 - )=0 ~+~3 ~)lt -ifR)AI~o - ) j-J

id

ot o - t-o aeNf+ -t ~ t- -+ 9 ~3 b11 _ ~11 L -+ ~ ~o

_~- -t -

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 28: Apostila de calculo  IV  1990

---r~L--~~_

oh)

f4ocircOu rI dAQlk ~ ~tt)( If() tQ~o ~oi -(lO~r ~ ~ ~ ltgt eoNV~v~ wI ~ Nt T

CgtO ~ ~~ ~ Ji~ Clt o N4ltcall ~~

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 29: Apostila de calculo  IV  1990

oacute~ IY(OacuteltL eo~ltVMSgt ~ chieNlNcruuQ ry-IJ~ ~ac CW-t~ du 1L ll) I J J ddj- i l z(l I ~ ) d 1

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 30: Apostila de calculo  IV  1990

~ =JJje2r fS1

~ ~ ~ (1l0lt1) ~ ~~

----- _ ---- shy

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 31: Apostila de calculo  IV  1990

--

~~ Ol ~ lt4t~ QtNagt46 ohoMtc ~~ ltUI -3- ~

0) J~ ~ dt + Jc1~di 3S j ~~ J~

D) ~~+ e~~ - -~-c ~72j ~~_ JCLjLi~J+ lli g-d

cl) 1iacutee~ dA +- ~1 tt1 +- ( e~ -+ J~) J ~

It) (~Li - J2) d~ + ( 3ecirc-- ~j) ct1

~~cio Q) lS~ =1)1

~i t)~ ~ ~j amp

3 ~ ~ ~J~ ~~CcedilJ

~i 6aj ~J ~~6 6laquo J - t

= shy- ~)otildeagrave ~ ~lt2 3)shy~ = 3- ~~ ~~ b~ shy

E txATA

~~o t51

~i 0-~(J ~j~Jy

~ I- ~J 07 1S~

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 32: Apostila de calculo  IV  1990

dJ ~ cl~+ ~1 ti) 4- (Q~jQ ) Jj

~ ~ Q ~ ~1 e

l5~~ ~~

~~ edshy~~O a-=~ ---- ~

~~ 61 ~-

~~ 6J- ~t 51

~ b~ - ~~ ~

YE- l E RiVI~ NACcedilP0 )f P)1J ccediliCcedilo CcedilgtolE IJA-L

tJt41ccedil q) ~ 1~~k+ J 1t1-t-J1 T Otilde8-i ltl~ NegtV-t4 ltgtshy

Ldey~ ~m ~ ltfJ ~J~ ~ ~o~ A( 213) e

lO t l a l ) -e eoao ~ ~ I lto-I =~ oIacuteINgt J ~~~ ~ t ~li VI ~ ie ~ QI~ AJ ~) ~Oo -c ~ocirciacuteamp a

-Vr-q J f~~oJ

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 33: Apostila de calculo  IV  1990

r

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 34: Apostila de calculo  IV  1990

-t~

s~ ~eacuteJ 2n aI ~ (-) Jv l hlampe~ -a -2 j

tJ1 2) )

~ -1 ~ lt~ _Ib - Uacute - 1lt e - -4 e 1 - ]

~vo shy

~aJ j ( 6Jj- ~() dI + ( 3~ gtsI ) oij oacuteP

aacuteP oJ~ de ~~QO ~l- ~~l j 1- ~~~

~ 00 ~~-1 OLOyt)) e

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 35: Apostila de calculo  IV  1990

Conro

~tyY ~ thlt Qobltt1q ~ lFWbce7 d~ 1 t T j~-o ~

Q OJotilde-itM

1Q) ltl~l gt rlUuml~middot + jalr a-lt)~

) -

0) 1tLt) t~ T t~k

d~ ~ dt ~ ti Ji a t

oudx = t+ L~) 4t

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 36: Apostila de calculo  IV  1990

A eacuteDe) 8 (1 Q)jJ

ehs i ~ 1shy

~r o

b) IJJ ~LlJJecirc17 t Jaf+ )~i ) d~ r1

i ~ampo

=1 (u~l+ ~nj+ JIZ) (Jc7~ dil + J~) I~

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 37: Apostila de calculo  IV  1990

gtt -3 4 l~~ ~+t -4 b =)

-~ _ -----

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 38: Apostila de calculo  IV  1990

l

( l

5J ~

tt 6

L3 (21f6 29~-b ~ 1 () ( -t- ~ 1) ~n ~-fgt~tc ccedil _ QI~ () hD oacuteaJlo llU ) ~~ r-- -fgtCcedilQ to o ~k

~~t~t~~~J~~~~ ~~~v~3~ ~~I ~ JeA~

w~ L 1t a lt 1 ~~ l dltC ~ Jjj- ltl~~)

~L -0-ltt i ~o

L~recirc WYVJ~)~= () ~ ~thillOJgt ~c-oO

~~O

~~~~~

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 39: Apostila de calculo  IV  1990

J PL A

- -shy -shy

I R I

c - -- -l _ - ___ - - I I - - - - t

b I0) K~(lt1) ~lt di

l~l Jfli) tlilli) dj Ji ~

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 40: Apostila de calculo  IV  1990

Imiddotmiddot --shy

~=-R Aacute)Q~ de ~~f)-)t) ~MA~ e ~ ~ UNI- ~O frAacutel

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 41: Apostila de calculo  IV  1990

I~~~~C ~Mocircdu-tffIIl( ltl t~~ M~~ JS ~(()I f) d~ 1

II Jjht)~( rd~~ ~(iacute j ) di ( G

i~~ ltl~~

tshy

-laquo

c-shy

ot b -

~ a

C

-

Q

b

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 42: Apostila de calculo  IV  1990

C)

Al 510) lL(j 1gt A(i I-middott) tgt (lti 5 ~ J 25)

~ ( ~ 3 i O) I 3-= J r ~$ l03 rI) ) ~ 6 lgt -1 l21 3) 4 l )

PR1)MC Ii)t C (2)310)~ 1r~It

1) liraquo) ~ 4 =1shy

~ E (3Q) ~g t1l3)~g) ~ 1 ocirc() E1 00 1-~~coeacute ocirc- aacuteo -j e A G

-ccedil ( Si tQ) j ~-~ ~lgt t== i l s ~J 50) r ( 3 3 o) 1 ~i-raquo -i (3 J

3) ~t)

iacute+ ( iu) () t b- B =- Ptl l J-l~ 8 )

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 43: Apostila de calculo  IV  1990

aI

J= 3 S~SdA I 5

v= - C(o~) lct- C) ~j)IIt OrXd) o~~ 01lt2

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 44: Apostila de calculo  IV  1990

copy

~bc ce 6 c~ I ( l CoV~~)r

J~ J( ampA l~ aacuteo ~(~~

9 ~ ~~~

(j) J 5Ilt ~l( i I elA lt jJ (h1) ~k lc - Iraquogt~ f5J

b

)raquo) l-ti-(lt4) d1- l lIacute I)]d~ ID CcedilLUumlj) dA~ 5J~ll(1)~

(sect0 J) J~(l -ti dA ~ Jf ~ llt 11 J4 + J J ~U1 I) dltl ~1 b~

oncL

~~L_~)

1-------------shy

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 45: Apostila de calculo  IV  1990

~

-~

UI J)j -cC- j~ d~ d-j

l i~il J l1~ 2

I ~ o

r 5~ I rI

01 t J~~i agrave~ dj -- jaacutel

~ d J )

i lt - tD ltl-ltl J

j-lf ~

j= ~ 1

ll- 1lt ~ lt4

ii l~

ltI1 - ~ o

~

) ~ (lt-)- gt

~ J2 ~0 ~- oD

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 46: Apostila de calculo  IV  1990

J__

f) i~ f kil~) ~I 1t (aacute t ccediltl Ich c

JCcedill~j)Jj

I

______

J

-shy-shy

o

jJ ~Xi) J1dt [dlt- Jh 1) dt ~

jt~~- fmiddot-middot-shy --~ i

1u ~ll) i - -

bull t i J~ ) ~f

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 47: Apostila de calculo  IV  1990

--

----

shy-~

bI ~1 ~trJo ~-

JJ ilIl cl1 d~ f

- ~~---~--------

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 48: Apostila de calculo  IV  1990

(~)~

~--t+-+=--==-t-----~~---J)~1 (

O

fmiddot

~ IIp I~ J1J rr (9 J

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 49: Apostila de calculo  IV  1990

foJlt dtdj

L shy - -

IoJ

lb JJ~~ Jj da rQ cL~yoi ltgt ~ vW-~

0( ~o ugtN) ~ ~

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 50: Apostila de calculo  IV  1990

e-)

eccedil ~ ~ ~~ 0 ~(-A (gt~IIO ~J d)

l

~)f~tAacutea ~~ shy )Jer~

G -~v) ~gt ~- cYJ -Q J) lt~ VJ( ccedil)

12 i 0)

----------------- _ -__-shy

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 51: Apostila de calculo  IV  1990

JcJ dt 11 ~= JJJIt

D ( JJ ~ dl1b

L - - -

o

~ ltf jJt4

r

~EJ ~ JJ ~t~

__~---+---~-f j

J

I

l

o CuacuteJIA do -k-MyVQ ~~ ~ Qc-~-ampo agrave ~- agraveo

) jo ~ _~

j~= 4 - ltf~ ri J~faacuter dt

lbl f~ Jd)h

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 52: Apostila de calculo  IV  1990

~gt( 4 _1 t_ )

- e

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 53: Apostila de calculo  IV  1990

3 -312 1

[ 3]_ Xl middot 4J

-2

(( J ) oJ JnJ djltk ((1

o ifj-- )b

j- 1 lb) JD J~ ~J1(d1i (j~ 8

c -xI

i J - ) I I

R (ocirc C ) j lt -) -) ~

e ) _ J- lt1

~1 j di ck 1t4It tJj NAl) ltiJAO O do(MiO f pk f ~Pjv ) Qr ~~ ~(X ~~-- t

~ 1 bull ~ ~ r

lt) iacute

~~~

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 54: Apostila de calculo  IV  1990

s

Cu

i

Jt Ji d~ ~( ~f dA + ~ (f_ dA ))L - ~j

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 55: Apostila de calculo  IV  1990

iL ( J

~ ~A -~Iop_OJfI __)gtJG

t 01n J i

__iJ I~_ u~)middot~_ j 5

V Pcl

O

j~ t~

5

J aidl = ~i11 tO

1o

Jl o

j5 di ltr J-t o

raquo)

~

( I d f

r ( ~ 6 -) -

kI~ O

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 56: Apostila de calculo  IV  1990

D

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 57: Apostila de calculo  IV  1990

I~ r~ 15 agravet~j middot

l JJ d~~J ~

~-~

~=~

-5

g s

QAacute

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 58: Apostila de calculo  IV  1990

Qf ij~ 7T

~ JJ~li$Ii) dA ~~ t

J ~~ ltt( UfJ)

LJ ~ Cu lJ) oltVUk

ir l U rgt- ) e j lu) 400 ~ lYi Ikl ~~-ltl Co M k~ ~~ ltk ~Oltdwm lto~~ ftM ~Qp R ~ ~ciM-0 ~ QV

3~~ wmk -1 o ~cbClJvIo

J ~ (l 1 ) ~ ~ ~ I 5l u) ()) ~~ fS1

~~ ~ o ( ~ fSJ

-J tr(Lhft)JjI lt JJ~i~~lI~~ J(~)rl ~~~ t-rJv

~ - -

~~de ~~~~ POLARES

i ( J c) fj shy

1 ~D p(Atildee-) ~

r) Jeh~ eshy

9

~~ANIOO ~etR1 ~ e l- 06 ~ 06) ~ ~~ fJ~ [olt-oltraquo

e- euro lS) ti J G iLlt p ~Oe- ~

j p IRM~

__ shy

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 59: Apostila de calculo  IV  1990

I

~1r lm~~ du~ (l

-ecirc-lr f~ 26

A I Jofd( ~1 1]oS aacute dt

J l( f Ccil amp

l j p~e-

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 60: Apostila de calculo  IV  1990

~= jJ~eshy

l j plJQM eshy

J JI 5 ) clt d~ Q)Iacute fl - lrl

Js)Jderi]Le ()1J5JJ pJpJamp 5U de- IpJP l o

PJP ~ tl 1P

secti = faJ10 -zlo (

I gJ) J pb- = 5 ~ 16 tlid~ j middot 30J~ct ~ ~1I =~iacute1 U V]lt

(- - shy_~ ~ CcedillJL (uumlc~ dRchLltoacuteu dc tmiddot middotru~() ltgt0JoD dAacute eacutegtliacute~

cio ~~~hO

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 61: Apostila de calculo  IV  1990

- Vz f~~~j)d fi = S) (~-~) d~

1fl X ~Ix b

j pAlhA

-2 - r=6 5=0 -shy ~f

j 2 ---to ~ a

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 62: Apostila de calculo  IV  1990

~ -

i _I

I 7

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 63: Apostila de calculo  IV  1990

I

Jjiacute

1p

L 1 1-

D

-r )

tJA J pfI

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 64: Apostila de calculo  IV  1990

~ j

1 Joacutefmiddot ) -

~

Je fP

j- jI =a-J

) I~p ri o

I ) fP Jrd( shy~

~

-1 ~

I f

1-

o

~J 1

~ r iacutei

~

- ~o

f ~JjJJ

- ~--- ------- ~

r ~a

--~--------_ --_--~

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 65: Apostila de calculo  IV  1990

A l g r n ~ 4-

1 _ -Jfgtlt ~ j ~~)1 (l

0 - 3

A-

~ i

j

amp(

I I

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 66: Apostila de calculo  IV  1990

-Qshy

))30 4 E~r ~ 5~ f~-

----1-e~-~-- t 10

A-(iO) ~lJlO) t (~n1)

Jfil l fid j O -

Jigte )l O - Il ~

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 67: Apostila de calculo  IV  1990

jc = i1

-rtdL 1 _~ laquo--1 - i LIA I~L -J2- (0( shy1

- i _ ( 1- z lt ~) ~ - i - ~t ~ ln ~ - e --L LV 2

iacute JAtilde6 +56 + f eacuteAgrave O-t ~lYlz - ~- ~ln e laquoLY2 - 2

JliacutePlt E~ OtildeP y o

Jocircp j O - bull omiddot ~)L

~ t 113 J- = - k = O S amp ~ feacute JQ dj - J o 1ai = ~J ~l

() o

v~

t

~ [~k- ~J2 ~~-1-Z L~~ a

--v- ~

o i- aLnz

GlOlO) O (~)et) ~ l ~IO) c lOI i-)

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 68: Apostila de calculo  IV  1990

Jacmiddot tcl~ shyL

-1- eecirc _ L12111 - -e- (i_i

-0deg

t- dll = J~ O ~ JF fVigt

~ 6) l 0 -lo dl o

J) - d) )- o o

e 0+ -i- e~o a e - e

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 69: Apostila de calculo  IV  1990

I

1(0-t1soVaWiBt1e

JjeuroJl Jalt1 ~ ele ftt1I ~~

~ ~i~ 7-l+ f +J -laquo2 O

lt l

CA-1Q+~ R

~ft vq R

J~= ~R

Y= t~ ampfl

evvcr~ c-x bull

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 70: Apostila de calculo  IV  1990

-t~ k s-H-middot~ J ~)CJlt

_ S+~Q~ ~~e~w--h

-- p - i

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 71: Apostila de calculo  IV  1990

I

~ ~ fJ - _~

iacutelte fltlO~qo ~J

() ~Oacute I 00 f) u) - + Q COegt t~ 1)QI(vJ t uG (01()

~~ R- J

J E [- ~ I 1fit1 - 11l

1 bull

jJ ~ 1gt-- -0~A V --J= u~ o~ ~~ 1r~

iJ+ jt ~ Q()~J + u~ )QM~J

t- = u t + ~) = ~tl- ]~ -= u

~~~ f 17 otilde-=~ ~1-+4lt

_____~

R

l~ uumllt Q() J

Qlt- j~ I ugt- cl C I -li

~

~ --_shy

__~S~e Q~Ul

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 72: Apostila de calculo  IV  1990

) +t-) ~~~ ~ ~ s(~J ) ~~o ) -R-t)i ~fl)o

-1 L l

tbull

bull

b) i--2Zc~ Otilde

~

S~~~ ~lJ-~CJln ~ M~-- ~ agrave~Q~~ l) I~gtl-~~+l

~=IJ 1-1 ~

~~ 1- ~u - V

~UumlM ~Lul)) uacute7 -+ ti -~u+ v

u E t -Decirc I -+ Ooacute) ~ ecirc (-00 -+tXJ

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 73: Apostila de calculo  IV  1990

C

J tJ

C)

) u euro [Q) z13

ft sshy t - T~ I ~YJ

iacutet- lA

j= -v

l d-l ~)

~ u4 J ~Jhr

l ) - 7 oa - uIr o-+ j J + u K

Su~V~ C~~-t ~~4t~cQ

1 lJe l-oamp) -toG) R I ltC l- 01 +olJ )

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 74: Apostila de calculo  IV  1990

ft bull

~u

~o

~

~=~ j = r

---~ 1- ult

5

3

j~ eJ

~~i---~

U f (-06+0)

~ E t (lI ~j()

--~-------

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 75: Apostila de calculo  IV  1990

~2 - ~lIJ -4 j ~ Beao v

~

IIZ __ IIE_Z J~ d v - ~ -~JltVshy

u e

~ ~-- _--_

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 76: Apostila de calculo  IV  1990

3 G-t - Qegtt 4 ~ bL _ 0t

I-Y

lU e tO~--~i shy bull

de_ ~ltf~~ ~(1 -)J- lTt1Ji oi DtO) t O- F-- ( 2()) e 6 (lt1)

~(umiddot~)

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 77: Apostila de calculo  IV  1990

lt+ 5u o

~ ~ Smiddot-r( -i 3 35 4

E b- _ F2 - 3~~ v j 1 B )~ j1 ~-431)4v

A~ lJ f ~43 ui v1 --- dll dv R

1 1 ~ ~

1 A bull

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 78: Apostila de calculo  IV  1990

~ -- ~

~1B1 JdV ) vagraveg

ltl ~li

o

(vA

b) InJJ- Jd~ o o

u

s[3l ---

~4

~ li J2 2-4

u~ shy

b

_ o

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 79: Apostila de calculo  IV  1990

r- ~ ~ ~ -- ~~T

~~ i~middot i~ c + ~ 5 J

5iacuteiacuteJ

~~ te-- t+ ~ j

l~

b) Jdi Jll+ 4)3) J1

j 1 5l2- If~ J1 o

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 80: Apostila de calculo  IV  1990

12 J+ 4 13) ~

~ 1(

(~+ s -Ct l-+4f)

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 81: Apostila de calculo  IV  1990

-eiiit $ilFI ~ fZfJ JfD 11shy

i~ ~~Qo ~lt11famp)1 ~ltA NJ20fr(l

~ ~Quacute~ JjJ l~i+l) dv

Y- f

To J ~~ ~~ ~~~ ~~~ l ~1 r=l

1- 1(

t-7+~=i

~ - 1 -

~l3--J

t(~rl

~ 0--~-1-Jl- ~- 1) t-fL( ~-rx - i)lO

3 ~3 2 shy--lIacute-t- 3~_ ~-k( + -16 - 3-nL- 1- Ut- lt

3

-

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 82: Apostila de calculo  IV  1990

l-i

Jltk Q

-- - -____--------- shy

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 83: Apostila de calculo  IV  1990

f tLty~ dA S~Q-~ de f) ~-te doe ~ llqV eJgt~Jltk oshy +-f s

laquoQAacute~IIo y~ eoS~~1IWOacute iM~~ ltk h ~-tcL~ ~ -eduy-UffA

Q o = iM~cr ~W l

iMiQjcJ~ ul ~Q O ~l1AT)= ~(-yt1 turo-)3 t ) (

t~

-- _--~--

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 84: Apostila de calculo  IV  1990

~J h1lt~ ~ a i) ~ Llt-lu) Jl) -lu)JE G _2 kJv

JJl~l+j-~)Jft~ JJ j o-l+ J _(~+l)~JJ 3)lt1I)-IlS ~~3 JA 5 R R I R

OacuteM~j + 3J( 3u~ j -+ ()1l~ (

O -t Su~ O

e l-r~~n ~ t

lA)1Il ~ 9gt11

~~ 1 ~ltui j -t I)l

OcircJ C ~ aJ t e lt3)llt llt

Su~~ o +

- lt cfr1r - ~ ~iIJ~~ ~

lt t311 -+ 3 ~ )(

~ (

3N 4 Ocirc cV ~

o + ~IJ 4

i~ r-r til-shy

~ _~--bull -~-~-__--bull- __

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 85: Apostila de calculo  IV  1990

L 2shy~ ~- ~-J

~-l - ~(f ) ~~ _k

~l- ~1

~dj =55imiddotIJ ~i+ ~ 4l ~

-Ic

I

~ ~_ ltL~ - jt1J~

tOlO) 1r=~=V

~ lt tV~ amp~2~-) ~-)2

-t ltiJ~yfll-)1tJ i~Qlagraveo v_~ (j Iacute~~ ~~ltC0 ~ vgt( J~I~JCJl ~Aacutegt-V_

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 86: Apostila de calculo  IV  1990

fMJ(J tu_ eJ~ uc fYC

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 87: Apostila de calculo  IV  1990

z t f t1l lt t H~ sf1F-

r~~~ ~- I - ~

)~ t~~~ A~ k~ ~-

~~~ GO~4l

tE TOfUAL- E(1cALA~ lE IOfUA 4 fiTQ (R) L

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 88: Apostila de calculo  IV  1990

- - ~t J 5i~ de po~~ ~~oo ~ ~ - shy~~ c ~ iS ~atilde-

3li l~

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 89: Apostila de calculo  IV  1990

~~~ ~ ~~

1

--C~OREA DA yER~f)q A f2E ~~~ -- -shy

~ pla ce ~

JIJ (Jrr)J =1Jil h Jl lt ~I T ~ - 0

)t itLWJ~ ul7+ ul ~)ts vt = IJE10R JNl~~O NO~MA otildeTb~OR ~

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132
Page 90: Apostila de calculo  IV  1990

1IJJf lnoJ) cl~ lt l ~ S ~

~ ~t~i~ ~ li ~+ l~)T J3 z V JEoR llTtl-RO NOIQfML e(TE~O~

f)t = li ltk + 2 d1-t- Vgt Jshy~C ~_ ~ de CoM~IIO olt

gt (1--- __ Jl~J-

o

  • p129
  • p130
  • p131
  • p132