CASTRUCTOR'S RESOURCE MANUAL EIGHTH EDITION ALCULUS Varbery, Purcell Rigdon PRENTICE HALL, Usyer Sale River, NJ 07858 xcculive fulton: Geouge Label Editorial Awistant: Gale A. Fans Special Projects Manager: Barbers A. heresy Production Euilor: Weady Rives Supplement Cover Manager: Paul Gaurhan Supplement Cover Designer: PM Warkshop I Manufacturing Buye - Alan Fischer © 2000 by Presse Hall ‘Upper Sale Iver, NI 67458 All rights rexerved, No part of tis hook may he reproduced, im any Cocuca Dy AM? meas, ‘without permission in weting tenn Che publisher. Printed ia the Unit States of Ameria weatess ISBN 0-23-085140-% Prentice Hall Irferuatiazal (UX) Liited, London Preotice Hall al Aneta Ply. Tnitea, Sjdoer Preatice Hall Canada. Sne., Torarie, Prego Hall Bizpancamcticana, S.A. Mexico Prentie Hall of India Private Limited. New Delhi Pearsoa Education tia Ple, Lid. Singapore Preatice-Full of Japan, The, Tokyo Faitora Prentice-Hall do Graal, Lida, Rio de Jans Contents SOLUTIONS Preliminares Functions and Limits “The Derivative Applicat one of the Derivative The Integral Applcatione of the Integra. Transcendental Functions Techniques of Integration Indeterminate Forme and Improper Integrals Infinite Series Numerical Methods, Apprenimations Conies and Potar Coordinates Geometry in the Plane, Vactors Geometry in Space, Vectors The Derivative in n-Space The Integral in n-Space Vector Caleulus Differential Equations PRINTED TEST BANK VE cE oe Spee r ] Prelirninaries 4.1 Concepts Review 1. sonal 3. ea 4, theorem Problem Set 11 1 acuaindees-aeaes Tiserenis 2 aaa) s2-4e5] size) 2928) =65 _ sav] =30) Sass 9202-71 2436-26) 2501) HS a geinenapeaen 2 - ts, [V5+s8](5-)- 5] -(5? 53 Instucto’s Resource Manus! Section 1.4 2h Quit }= det eda aes aad aan4 (2e-302-3) 2, (de-UINe-)= LF 284-3877 ie 677 2s, Section 4.4 26 Gr prs 394 3H24 3) 2? Dress, vine 242 ser e194 7 centage sie 27 Ge metsy u. » eM ee ee mrarereen aD ace rest 2. Dy ti” Gti) sy) 2 Bipeiy Wy Lysneysh Gy nos) yr tonyniagt aioe Gy FHiey= Instuctor's Resource Maral ~ ays by? 20942 “Eee ete =D) r 2 2 caren) an Eoacerrer) etka 0¢e= 2} 8 se une asa o0-0 bie undeined. 3 0 3 1 2 ieundetnes ao a1 361 shen D= 0-2, bis meninges because a could beaoy 3: mbar, No 0 Single value satisties a Mx Be TBalse he o> =U Te re -8> Wi, E>: Te 6 HTH PR ae 739° “ies! Instructors Rescue Manual * 4, 7 Soft. BE MH eae Ban a a achat eqbandul <t8,so2 <6? bovat fe > eetceta thera pesetberh actihay a ined o<d a Isaways roe fea me Tie, Wa inpeste dee oie bales Toke x2. Ten Po doured. ee Fake; Take v= yh & Te 9-2 seownandprime te Trae; Lelie any bee Take yet alta yo? Fase: Three vn aunbe larger har fe Te; ‘renetemée atuaanty clos 00 be Tae 2a bina aba slot Ven ita thon nee neg sh ‘hat n= eT. Thee Peake tf ak art? 42841 Section 14 4 4 “6 Prove a esomapeiive Suppose it ben, Then thee age ue at nedk The nyt ae ey “Tous 13 is er se ares (8) and prove thaws fad only if 0? inte yet be ta eae) th gare uf the aber isthe prose of pes hich gororay even wate OF SS BP o2e one Seto of p? mus! ust a esa uber of = gs Since theprme tie, 292 would not he ald ad 2 = sat bo iran ag = Pi Saceteprine fasrrs of p? moe aeut an even umber of sa Zag times, 34 wouké ro. be va and 2 = 3 @ must be ition ate. bop. ard be mate winters, se 2 and i an eational 262 222 This sums 4 Boy the gunn fama aumbers sits alba ‘sional. Ventas ations mer ap ag be 2 2 singe de ae umm isa trl number, he product rata macs. a 9+ 3 in Section 2.4 0395-2: rma 1 irons Ao eGR esas inion OEMs -150 5 rtm. 6 NB: cmeoral “Phe sum of to sonal marchers lis iatonal. the muzibers are ative icin Se gum is. ie rte Hye ore paved quate. Us pice factors ‘would occur even numbers of ties Im iran pore aqua, same fcters wil ecco omer f lec: and sn wil be ational slo vi a4 1anssis rational YB =v v= 2.18165 ic iraiona gg 821149407 ig ieiona s Convene °F gel an A in his cout, thst 1 9 ll ofthe hemor, CConmaposv UF Uo tan A in his our, ther Lebar da a: ot he bomewerk. Convenes Ii an integer ther 2 ral nubs, Contposfve 1 i onan ieee, ‘hen «sant rel umber. fe Convenes AARC isan soscetes ial, thee ABC" isa culate ‘Ceamaposhive:f ABC ixnutsn soma wnngls, ten AABC ie 7040 eine ae Instructor's Resource Manl 1.2 Concepts Review J. 995. erepeny B20. (05 ope SM, 4 tal Problem Set 1.2 oss ‘FEcoq000 u Inctructor's Rescurca Manual 230153 shires wos a Section 4.2 “ 546153 ssfitcecoo wwe 2. xvas. oun = 123128123. aun, 281712, d x= 2 86865656. Whee = 256585656. 28556 1b, v=3909007 ns = 392929280. 2920292 yet Section 1.2 1 = 0199059. os ~ 1259998 os _1.99999 Pe TE wt 1, 22039989, ts = 9.99848 x 23950%, ea % % 30 (4. Those ations berth: canbe spree bye lee ec loses iy ben, - o(é} seve only ned lent 23 ton (2) -tor war mene satay ne cecinating decimls is ston 2 serminating lesa, s0 (57° and (.2)" and hheawe dc pode 4. i 4 erasing Ascircat, Toos © nas vermiwing dst a expansion, 18, Avatars wil wary. Pome ase 000001 I sotto 16, Sirallet postveintepe~ [Tere ism lle! pose toro: reieal aunbec 17, Ananera wil yon. hese awe 18138101001 18, Those fa eal mmr berwean 60. (reposting ad |. DIM. amd Lepesene the samme seal wer 18, Iratons! 20, Arye wil vary. Posibeanswer onl, fan 2, G5 at «zuswons lnstuctar’s Resource Manu BH, P= 2.9270) 00210) 543 in? 35 a AC ee2r 206 RSA? D Ane=2S @1Hs ne ALES 27: 1474067 a Mn aaaa 26 thee ear-10 sessed srineesher liter tive peat) {o00:)(s.25e30 *) = oq1ezrs2i4s are) a7, esa e1— tn o0m6sr744752 a Ace 28 ide? Ze = 3.061591807 be Av eseist. Tez? 29. Let andb be eal cums wit <b, Lee Ares 1eZ50 505886 beamlines ht seis Uncb- ata Sa (kk > Ob. Since A qretatsnemez onsrpy al flees tat eo a e121 cen ‘pte cae a ast een mes ha by ES such she: ky 2B onl thy line e. Theo 1 fet sy tay £8. thes choose Tas, 0< Se" otherwite cose 7 = ct 5 2 Anewcit will vicy Pole nent: =120 8 a . st = 4000 i s280® — 24 120,000 6 guste = 2 « 221,120.00) 3 132,700,574 the vper booed 2, 22, Anaver wil vary. Pose abies 2 eI IN ny yg 5 Tol 60 a4 M305 82% x20 ne rine ag 88 a 20 3 38 349.000 bss 38, a, Asst wll vay, Posieahtoer An compte oi Peete Ban ema SeSet0:2 coo mone z ere he eas upper ound i 5, sich 293,00 45198 93 rei bella ‘oma fn ai (in ches Ine THIS Iz 1atin? ener of tooed fs: BENIN p51e4) bowl Instructor's Resnaree Mania! Section 12