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

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94 D . CHAPTER 11 INFINITE SEQUENCES AND SERIES (c) 0.00008 ~------------~ y = IR,(x)l From the graph of jR3(x)l = le~ 2 error is less than 0.000 051 on [0, 0.1]. - T3(x) l, it appears that the 21. n J
SECTION 11.11 APPLICATIONS OF TAYLOR POLYNOMIALS D 95 · 1 3 1 s Bth I · s · 27. sinx = x- 3!x +Six - · · ·. y e A ternatmg enes Estimation Theorem, the error in the approximation sin x = x - ~x 3 is less than I ;,x 5 1 < 0.01 ¢:} lx 5 l < 120(0.01) ¢:} lxl < (1.2) 115 ~ 1.037. The curves y = x - ix 3 andy= sinx- 0.01 intersect at x ~ 1.043, so the graph confirms our estimate. Since both the sine function 0.9 r-------------~~~~--~ y=sinx+ o.oV / / / y=x-kx 3 / ~ 'fooox-O.QJ 0.9 "-L,__L,.:...__ _.__________./ 1.2 0.8 and the given approximation are odd functions, we need to check the esti~ate only for x > 0. Thus, the desired range of . values for xis - 1.037 < x < 1.037. x 3 x 5 x 7 29. arctan x = x - 3 + 5 - 7 + · · · . By the Alternating Series Estimation Theorem, the error is less than l -~ x 7 1 < 0.05 ¢:} y =arctan x + 0.05 jx 7 j < 0.35 ¢:} lxl < (0.35? 17 ~ 0.8607. The curves y = x- tx 3 + kx 5 andy= arctanx + 0.05 intersect at x ~ 0.9245, so the graph confirms our estimate. Since both the arctangent function and the given approximation are odd functions, we need to check the estimate only for x > 0. Thus, the desired range of values for xis - 0.86 < x < 0.86. - 1 y = x - .!. x 3 + .!. xs 3 5 31. Let s(t) be the position function of the car, and for convenience set s(O) = 0. The velocity of the car is v(t) = s' (t) and th~ acceleration is a(t) = s" (t), so the second degree Taylor Polynomial is T2(t) = s(O) + v(O)t + a~O) t 2 = 20t + t 2 . We estimate the distance traveled during the next second to be s(1) ~ T2(1) = 20 + 1 =21m. The function T 2 (t) would not be accurate over a full minute, since the car could not possibly maintain an acceleration of 2 m/s 2 for that long (if it did, its final speed would be 140 m/ s ~ 313 mi/ hl). 33. E = ~2 - (D!d)2 = ~2- D2(1:d/ D)2 = ; 2 [1 - (1+ ~r2l We use the Binomial Series to expand (1 + d/ D ) - 2 :. when D is much larger than d; that is, when P is far away from the dipole. 35. (a) If the water is deep, then 27rd/ L is large, and we know that tanh x -+ 1 as x -+ oo. So we can approximate tanh(27rd/ L) ~ 1, andsov 2 ~ f!L/ (27r) ¢:} v ~ ..jgLj (21r). © 2012 Cengage Learning. All Rights Reserve-d. May not be SC41lncd, copied, or duplicaled, or poSied 10 a publicly accessible website. in whole o r in part.
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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. ~
Page 51 and 52: 0 PROBLEMS PLUS l lt sin u dx cost
Page 53 and 54: 11 . D INFINITE SEQUENCES AND SERIE
Page 55 and 56: SECTION 11.1 SEQUENCES 0 47 35. a,.
Page 57 and 58: SECTION 11.1 SEQUENCES D 49 71. Sin
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Page 67 and 68: SECTION 11.3 THE INTEGRAL TEST AND
Page 69 and 70: , SECTION 11.3 THE INTEGRAL TEST AN
Page 71 and 72: SECTION 11.4 THE COMPARISON TESTS D
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Page 77 and 78: SECTION 11.6 ABSOLUTE CONVERGENCE A
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Page 87 and 88: SECTION 11.9 REPRESENTATIONS OF FUN
Page 89 and 90: SECTION 11.9 REPRESENTATIONS OF FUN
Page 91 and 92: SECTION 11.10 TAYLOR AND MACLAURIN
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Page 99 and 100: SECTION 11.11 APPLICATIONS OF TAYLO
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Page 105 and 106: CHAPTER 11 REVIEW 0 97 J'(xn)(xn -
Page 107 and 108: CHAPTER 11 REVIEW 0 99 oo f (n) (O)
Page 109 and 110: CHAPTER 11 REVIEW 0 101 l 23. Consi
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Page 113 and 114: D PROBLEMS PLUS 1. It would be far
Page 115 and 116: CHAPTER 11 PROBLEMS PLUS D 107 l 9.
Page 117 and 118: CHAPTER 11 PROBLEMS PLUS 0 109 x x
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D PROBLEMS PLUS 1. Since three-dime
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l CHAPTER 12 PROBLEMS PLUS 0 149 Eq
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13 D VECTOR FUNCTIONS 13.1 Vector F
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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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