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

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44 D CHAPTER 10 PROBLEMS PLUS a 2 d 2 -b 2 c 2 ad+ bc d h . bad+be ad'-t-be => X = b(ad _be) = - -b- an t e y-va 1 Ue IS a --b- = --a- · S 1m1 . . 1 ar 1 y, t h e tangent 1 . me mtersects . y = -ax b at (be --b-, - ad --aad - be ) . Th e m1 .d pomt . o ftl 1ese mtersect1on . . pomts . 1s . ( 1 (ad+bc be- ad) 1 (ad+ be ad-be)) (12bc 12ad) . 2 --b- + --b- • 2 --a- + --a- = 2 b , 2--;;:- = ( c, d), the pomt of tangency. Note: Jf y = ·o, then at (±a, 0), the tangent line is x = ± a, and the points of intetsection are clearly equidistant from the point of tangency. ® 2012 Cengnge learning. All Rights Reserwf. Mny not be scanned. eopictl. or duplicated, or posted ton publicly accessible website, in whole or in pilrt.
11 . D INFINITE SEQUENCES AND SERIES 11.1 Sequences 1. (a) A sequence is an ordered list of numbers. It can also be defined as a function whose domain is the set of positive integers, (b) The terms a,. approach 8 as n becomes large. In fact, we can make an as close to 8 as we like by taking n sufficiently large. (c) The terms an become large as n becomes large. In fact, we can make an as large as we like by taking n sufficiently large. 2n . { 2 4 6 8 10 } { 4 3 8 5 } 3. an = n2 + 1, so the sequence IS 1 + 1' 4 + 1 ' 9 + 1' 16 + 1' 25 + 1' . . . = 1, 5' 5' 17' 13 ' . . . . (-1)n- l . . { 1 -1 1 -1 1 } { 1 1 1 1 1 } · 5. an = 5n , so the sequence IS 51' 52' 53 ' 54' 55 '... = 5' - 25' 125'-625' 3125'... . 1 . {1 1 1 1 1 } {11 1 1 1 } 7. ~ = (n + 1)!, so the sequence IS 2!'"3!' 4f• 5!' 6!'... = 2' 6' 24 , 120, 720'... . 9. a 1 = 1, a,,+ 1 = 5an- 3. Each term is defined in terms of the preceding term. a2 = 5a1 - 3 = 5(1)- 3 = 2. a 3 = 5a2 - 3 = 5(2) - 3 = 7. a4 = 5a3 - 3 = 5(7) - 3 = 32. as = 5a4 - 3 = 5(32) - 3 = 157. The sequence is {1, 2, 7, 32, 157, ... }. a3 Q.4 = --= 2/5 2 = 1 + a3 1 + 2/5 7• a 5 = 1 : 4 a 4 =:' 1 ~;/7 = ~- ,The sequence is {2, ~. ~. ~' ~ •... }. The denominator of the nth term is the nth positive odd integer, so an= - - 1 -. 2n-1 15. { - 3, 2, -1, ~,- ;~, ... }. The first term is -3 and each term is - ~ times the preceding one, so a,. = -3 ( -~ f - 1 . 17. { ~, -~,%,- 1 :, 2 5~, ... }. The numerator of the nth term is n 2 and its denominator is n + 1. Including the alternating signs, n2 wegetan = (-1)n+l __ _ n+1 ® 2012 Ccngage Learning. All Rights Reset\'ed. Moy not be scnnned. copied, or duplicated, or posted to u publicly accessible website, in whole or in par1. 45
Page 1 and 2: - STUDENT SOLUTIONS MANUAL for STEW
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Page 5 and 6: D ABBREVIATIONS AND SYMBOLS CD cu D
Page 7 and 8: viii o CONTENTS 12.4 The Cross Prod
Page 9 and 10: 10 D PARAMETRIC EQUATIONS AND POLAR
Page 11 and 12: SECTION 10.1 CURVES DEFINED BY PARA
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Page 15 and 16: SECTION 10.2 CALCULUS WITH PARAMETR
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Page 39 and 40: x2 y2 y2 a:2 _ a2 b 61. ;_2 - - = 1
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Page 51: 0 PROBLEMS PLUS l lt sin u dx cost
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SECTION 11.11 APPLICATIONS OF TAYLO
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CHAPTER 11 REVIEW 0 97 J'(xn)(xn -
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CHAPTER 11 REVIEW 0 99 oo f (n) (O)
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CHAPTER 11 REVIEW 0 101 l 23. Consi
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49./- 1 - dx = -ln{4- x) + C and 4-
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D PROBLEMS PLUS 1. It would be far
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CHAPTER 11 PROBLEMS PLUS D 107 l 9.
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CHAPTER 11 PROBLEMS PLUS 0 109 x x
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112 0 CHAPTER 12 VECTORS AND THE GE
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120 D CHAPTER 12 VECTORS AND THE GE
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136 D CHA~TER 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 16.8 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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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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