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

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90 0 CHAPTER 11 INFINITE SEQUENCES AND SERIES 00 75. (a) g(x) = :L; 00 (k) x"' => g'(x) = :L; (k) nx"- 1 , so n~ n n~ n 00 00 (1 + x)g'(x) = (1 + x) :L; 00 (k) nxn- (k) (k) 1 = :L; nx"'- 1 + :L; nxn n=1 n n=1 n n = 1 n . . I Replace n with n = f: ( k ) (n 1 + 1)xn + f: (k)nxn + 1 ] n=O n+ n = O n [ in the first series 00 00 _ k(k-1)(k-2) .. ·(k-n+1)(k-n) n [ k(k- 1)(k - 2)···(k-n+ 1)] ,, - n~o (n + 1 ) (n + 1)! x + n~O (n) nl x 00 (n + l )k(k - '1)(k - 2) ... (k- n + 1) n = n~O (n+ 1)! . ((k -n)_+n]X = k n~o k(k - 1)(k- 2l! ... (k- n + 1) x" = k fo ( ~) x" = kg(x) Thus, g'(x) = k 1 g(x). +x (b) h(x) = (1 + x)-k g(x) => h'(x) = - k(l + x)- k- 1 g{x) + (1 + x)-k g'(x) = -k(l + x)-i.:- 1 g(x) + (1 + x)- k kg(x) 1+x = -k(l + x)-k- 1 g(x) + k{1 + x)-"'- 1 g(x) = 0 [Product Rule] [from part (a)] (c) From part (b) we see that h(x) must be constant for x E ( -1, 1), so h(x) = h(O) = 1 for x E ( -1, 1). Thus, h{x) = 1 = (1 + x)-k g{x) g(x) = {1 + x)k for x E ( -1, 1). 11.11 Applications of Taylor Polynomials 1. (a) J (x) t
SECTION 11.11 APPLICATIONS OF TAYLOR POLYNOMIALS D 91 I (b) X f To =T1 T2 = Ts T4 =Ta Te 1r 4 7f 2 0.7071 1 0.6916 0.7074 0.7071 0 1 - 0.2337 0.0200 - 0.0009 1T - 1 1 -3.9348 0.1239 -1.2114 3. (c) As n increases, Tn ( x ) is a good approximation to f ( x) on a larger and larger interval. n f(nl(x) j(n)(2) 0 1/x 1 2 1 - 1/ x 2 1 - 4 2 2/x 3 1 4 3 · - 6/x 4 3 - 8 3 J (n)(2) Ts(x) = 2::::: -- 1 - (x- 2)" ·n=O n. 1 1 1 3 = 2 - l (x - 2) + 4 (x- 2? - j_ (x- 2? 0! 1! 2! 3! = t- H x - 2) + ~(x - 2) 2 - fa(x- 2) 3 5. n J
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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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Page 51 and 52: 0 PROBLEMS PLUS l lt sin u dx cost
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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
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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
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Page 91 and 92: SECTION 11.10 TAYLOR AND MACLAURIN
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Page 101 and 102: 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 117 and 118: CHAPTER 11 PROBLEMS PLUS 0 109 x x
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142 D CHAPTER 12 VECTORS AND THE GE
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144 0 CHAPTER 12 VECTORS AND THE GE
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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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