Exercicios resolvidos James Stewart vol. 2 7ª ed - ingles

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102 0 ~HAPTER 11 INFINITE SEQUENCES AND SERIES 39. Use the Limi~ Comparison Test. lim I(~ )a,, I = lim n + 1 = Jim (1 + .!) = 1 > 0. n--+00 an n - oo n n-+oo n Since E Ia,. I is convergent, so is I: \ ( n : 1 ) a,. I, by the Limit Comparison Test. 41. lim I a,.+ll = lim [ lx + 21"+1 . n4" ,.] = lim [__2!:___ lx + 2[] = [x + 21 < 1 ¢:} lx + 21 < 4, so R = 4. n - oo an !'-oo (n + 1) 4"+ 1 lx + 21 n-oo n + 1 4 4 oo (x + 2)n lx + 21 < 4 ¢:? -4 < x + 2 < 4 ¢:? - 6 < x < 2. lfx = - 6, then the series E becomes . • n =l n 4" f: (- 4 4r = f: (- l )", the alternating harmonic series, which converges by the Alternating Series Test. When x = 2, the n=l 71. n = l n series becomes the harmonic series f: .!, which diverges. Thus, I= [- 6, 2). n=l n 43. lim I Un+l l = lim 1 2 n+ 1 (x- 3 )"+1 · y'n+3 ,., = 2 jx- 31 lim Jn + 3 = 2lx- 31 < 1 ¢:} jx- 31 < ~. n-oo a,. n-oo ../n + 4 2"(x - 3) n-oo n + 4 soR = ~- lx- 31 < ~ ¢:? · · oo 2"{x - 3}" -~ < x- 3 < ~ ¢:} ~ < x < ~ · For x =~. the series I: .;n+3 becomes · n =l n +3 45. I: ~ = I: ;/ 2 , which diverges [P = ~ $ 1), but for X = ~' we get I: ~ .which is a convergent n=O y n + 3 n=3 n n=O v n + 3 alternating series, so I = [ ~ , ~). n /("l(x) / (n)(:g) 1 0 sinx 2 1 cosx .il 2 - sin x 3 - cosx 4 sin x •. 2 1 - 2 _ _il 2 1 2 "C) {3) (7r) {4}C) sinx = f(~)+f'(~)(x-~)+!.____i_(x-~) 2 + / 6 (x-~) 3 +/ 6 (x - ~) 4 + ... 6 6 . 6 2! 6 3! 6 4! 6 47. - 1 +- 1 -X = 1 _ ~- X) = n~O (- x)" = n~O {-1)" x" for lxl < 1 2 00 => ~ =I: {-1f'x"+ 2 withR= 1. 1+x n = O © 2012 Ccngnge Learning. All RighiS R=n-.:d. May not be S
49./- 1 - dx = -ln{4- x) + C and 4-x I I I 1 1 1 1 00 (X)" 1/ oo x" 1 oo xn+1 4 - X . 4 1 - x/4 4 n=O 4 4 n=O 4" . 4 n=O 4"(n + 1} · --dx = - - - dx = - L: - dx = - E - dx = - E + C So CHAPTER 11 REVIEW D 103 1 00 xn+1 00 xn+1 00 x" . ln{4 - x)=-- 4 E ,.( 4 1 ) +C= - E 4 ,.+ 1( + ) +C = - 1 E n +C.Puttmg x=O,wegetC = ln4. n=O n+ n=O n n=1 n 4 oo x" . Thus, f(x) = ln{4- x) = ln4- E rt=1 n 4 Another solution: " . The series converges for Jx/ 41 < 1
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- STUDENT SOLUTIONS MANUAL for STEW
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.. BROOKS/COLE ~ I ~~r CENGAGE Lear
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D ABBREVIATIONS AND SYMBOLS CD cu D
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viii o CONTENTS 12.4 The Cross Prod
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10 D PARAMETRIC EQUATIONS AND POLAR
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SECTION 10.1 CURVES DEFINED BY PARA
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SECTION 10.1 CURVES DEFINED BY PARA
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SECTION 10.2 CALCULUS WITH PARAMETR
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SECTION 10.3 POLAR COORDINATES 0 13
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SECTION 10 .~ POLAR COORDINATES 0 1
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SECTION 10.4 A~~S AND LENGTHS IN PO
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SECTION 10.4 AREAS AND LENGTHS IN P
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SECTION 10.4 AREAS AND LENGTHS IN P
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SECTION 10.5 CONIC SECTIONS 0 27 5.
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SECTION 10.5 CONIC SECTIONS 0 29 35
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x2 y2 y2 a:2 _ a2 b 61. ;_2 - - = 1
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SECTION 10.6 CONIC SECTIONS IN POLA
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CHAPTER 10 REVIEW 0 35 the length o
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CHAPTER 10 REVIEW 0 37 EXERCISES 1.
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CHAPTER 10 REVIEW 0 39 25. x = t +
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CHAPTER 10 REVIEW 0 41 2 2 . 45. ~
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0 PROBLEMS PLUS l lt sin u dx cost
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11 . D INFINITE SEQUENCES AND SERIE
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SECTION 11.1 SEQUENCES 0 47 35. a,.
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SECTION 11.1 SEQUENCES D 49 71. Sin
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Page 67 and 68: SECTION 11.3 THE INTEGRAL TEST AND
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Page 71 and 72: SECTION 11.4 THE COMPARISON TESTS D
Page 73 and 74: SECTION 11.5 ALTERNATING SERIES 0 6
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Page 77 and 78: SECTION 11.6 ABSOLUTE CONVERGENCE A
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Page 81 and 82: 17 lim I an+l I= SECTION 11.7 STRAT
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Page 87 and 88: SECTION 11.9 REPRESENTATIONS OF FUN
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Page 91 and 92: SECTION 11.10 TAYLOR AND MACLAURIN
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Page 107 and 108: CHAPTER 11 REVIEW 0 99 oo f (n) (O)
Page 109: CHAPTER 11 REVIEW 0 101 l 23. Consi
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Page 153 and 154: D PROBLEMS PLUS 1. Since three-dime
Page 155 and 156: l CHAPTER 12 PROBLEMS PLUS 0 149 Eq
Page 157 and 158: 13 D VECTOR FUNCTIONS 13.1 Vector F
Page 159 and 160: SECTION 13.1 VECTOR FUNCTIONS AND S
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SECTION 13.1 VECTOR FUNCTIONS AND S
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SECTION 13.2 DERIVATIVES AND INTEGR
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SECTION 13.2 DERIVATIVES AND INTEGR
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SECTION 13.3 ARC LENGTH AND CURVATU
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SECTION 13.4 MOTION IN SPACE: VELOC
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2 SECTION 13.4 MOTION IN SPACE: VEL
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CHAPTER 13 REVIEW D 173 43. The tan
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5. f~(t 2 i +tcos 1rtj +sin 1rt k )
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CHAPTER 13 REVIEW 0 177 23. (a) r (
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180 0 CHAPTER 13 PROBLEMS PLUS (-2a
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182 0 CHAPTER 13 PROBLEMS PLUS vect
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184 0 CHAPTER 14 PARTIAL DERIVATIVE
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196 D CHAPTER 14 PARTIAL DERIVATIVE
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D PROBLEMS PLUS 1. The areas of the
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15 D MULTIPLE INTEGRALS 15.1 Double
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SECTION 15.2 ITERATED INTEGRALS D 2
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l SECTION 15.3 DOUBLE INTEGRALS OVE
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SECTION 15.3 DOUBLE INTEGRALS OVER
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SECTION 15.3 DOUBLE INTEGRALS OVER
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61 . Since m :S j(x, y) :S M, ffD m
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SECTION 15.4 DOUBLE INTEGRALS IN PO
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SECTION 15.5 APPLICATIONS OF DOUBLE
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SECTION 15.5 APPLICATIONS OF DOUBLE
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SECTION 1505 APPLICATIONS OF DOUBLE
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-I SECTION 15.6 SURFACE AREA 0 267
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SECTION 15.7 TRIPLE INTEGRALS 0 269
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SECTION 15.7 TRIPLE INTEGRALS D 271
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Therefore E = { (x, y, z) I -2 ~ X~
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43. I,. = foL foL foL k(y2 + z2)dz.
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SECTION 15.8 TRIPLE INTEGRALS IN CY
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M xv = I~1f I: I:2 6 - 3 r 2 (zK) r
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SECTION 15.9 TRIPLE INTEGRALS IN SP
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SECTION 15.9 TRIPLE INTEGRALS IN SP
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(b) The wedge in question is the sh
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SECTION 15.10 CHANGE OF VARIABLES I
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CHAPTER 15 REVIEW 0 289 15 Review C
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CHAPTER 15 REVIEW 0 291 l 9. The vo
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CHAPTER 15 REVIEW D 293 33. Using t
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49. Since u = x- y and v = x + y, x
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298 D CHAPTER 15 PROBLEMS PLUS To e
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300 0 CHAPTER 15 PROBLEMS PLUS 13.
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16 0 VECTOR CALCULUS 16.1 Vector Fi
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SECTION 16.2 LINE INTEGRALS 0 305 2
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SECTION 16.2 LINE INTEGRALS 0 307 (
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SECTION 16.2 LINE INTEGRALS D 309 3
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SECTION 16.3 THE FUNDAMENTAL THEORE
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SECTION 16.4 GREEN'S THEOREM D 313
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SECTION 16.4 GREEN'S THEOREM 0 315
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8 8 8 (b)clivF = 'V ·iF=- (x+yz) +
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SECTION 16.5 CURL AND DIVERGENCE 0
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SECTION 16.6 PARAMETRIC SURFACES AN
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that is, D = {( x, y) I x 2 + y 2 :
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SECTION 16.7 SURFACE INTEGRALS 0 32
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SECTION 16.7 SURFACE INTEGRALS 0 33
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SECTION 16.8 STOKES' THEOREM 0 333
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dS SECTION 16.9 THE DIVERGENCE THEO
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CHAPTER 16 REVIEW 0 337 27. JI 5 cu
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CHAPTER 16 REVIEW 0 339 TRUE-FALSE
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CHAPTER 16 REVIEW D 341 Alternate s
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344 0 CHAPTER 16 PROBLEMS PLUS Simi
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3.c6 0 CHAPTER 17 SECOND-ORDER DIFF
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348 0 CHAPTER 17 SECOND-ORDER DIFFE
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352 D CHAPTER 17 SECOND-ORDER DIFFE
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356 D CHAPTER 17 SECOND-ORDER DIFFE
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0 APPENDIX Appendix H Complex Numbe
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APPENDIX H COMPLEX NUMBERS 0 361 43
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Exercicios resolvidos James Stewart vol. 2 7ª ed - ingles

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