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

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D · CONTENTS 0 10 PARAMETRIC EQUATIONS AND POLAR COORDINATES 1 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 7 10.3 Polar Coordinates 13 10.4 Areas and Lengths in Polar Coordinates 20 10.5 Conic Sections 26 10.6 Conic Sections in Polar Coordinates 32 Review 35 Problems Plus 43 0 11 INFINITE SEQUENCES AND SERIES 45 11.1 Sequences 45 11.2 Series 51 11.3 The Integral Test and Estimates of Sums 59 11 .4 The Comparison Tests 62 11.5 Alternating Series 65 11 .6 Absolute Convergence and the Ratio and Root Tests 68 11 .7 Strategy for Testing Series 72 11.8 Power Series 74 11.9 Representations of Functions as Power Series 78 11.10 Taylor and Maclaurin Series 83 11.1 1 Applications of Taylor Polynomials 90 Review 97 Problems Plus 105 0 12 VECTQRS AND THE GEOMETRY OF SPACE 111 12.1 Three-Dimensional Coordinate Systems 111 12.2 Vectors 114 12.3 The Dot Product 119 0 201 2 Ccogagc Learning. AU Rights Rcscn-cd. May not be scanned, copi~.:d, or duplicouccJ, or posletl to a publicly acc.:es.!~ible website, in whole or in p!U1.. vii
viii o CONTENTS 12.4 The Cross Product 123 12.5 Equations of Lines and Planes 128 . 12.6 C,ylinders and Quadric Surfaces 135 Review 140 Problems Plus 147 0 13 VECTOR FUNCTIONS 151 13.1 Vector Functions and Space Curves 151 13.2 Derivatives and Integrals of Vector Functions 157 13.3 Arc Length and Curvature 161 13.4 Motion in Space: Velocity and Acceleration 168 Review 173 Problems Plus 179 0 14 PARTIAL DERIVATIVES 183 14.1 Functions of Several Variables 183 14.2 Limits and Continuity 192 14.3 Partial Derivatives 195 14.4 Tangent Planes and Linear. Approximations 203 14.5 The Chain Rule 207 14.6 Directional Derivatives and the Gradient Vector 213 14.7 Maximum and Minimum Values · 220 14.8 Lagrange Multipliers 229 Review 234 Problems Plus 245 0 15 MULTIPLE INTEGRALS 247 15.1 Double Integrals over Rectangles 247 15.2 Iterated Integrals 249 15.3 Double Integrals over General Regions 251 15.4 Double Integrals in Polar Coordinates 258 Q 2012 Ccngage Learning. All Rights Rcscn·ed. May not be scanned, copied, or dU!>licaLcd. or posted to a publicly accessible website, in whole or in part.
Page 1 and 2: - STUDENT SOLUTIONS MANUAL for STEW
Page 3 and 4: .. BROOKS/COLE ~ I ~~r CENGAGE Lear
Page 5: D ABBREVIATIONS AND SYMBOLS CD cu D
Page 9 and 10: 10 D PARAMETRIC EQUATIONS AND POLAR
Page 11 and 12: SECTION 10.1 CURVES DEFINED BY PARA
Page 13 and 14: SECTION 10.1 CURVES DEFINED BY PARA
Page 15 and 16: SECTION 10.2 CALCULUS WITH PARAMETR
Page 21 and 22: SECTION 10.3 POLAR COORDINATES 0 13
Page 27 and 28: SECTION 10 .~ POLAR COORDINATES 0 1
Page 29 and 30: SECTION 10.4 A~~S AND LENGTHS IN PO
Page 31 and 32: SECTION 10.4 AREAS AND LENGTHS IN P
Page 33 and 34: SECTION 10.4 AREAS AND LENGTHS IN P
Page 35 and 36: SECTION 10.5 CONIC SECTIONS 0 27 5.
Page 37 and 38: SECTION 10.5 CONIC SECTIONS 0 29 35
Page 39 and 40: x2 y2 y2 a:2 _ a2 b 61. ;_2 - - = 1
Page 41 and 42: SECTION 10.6 CONIC SECTIONS IN POLA
Page 43 and 44: CHAPTER 10 REVIEW 0 35 the length o
Page 45 and 46: CHAPTER 10 REVIEW 0 37 EXERCISES 1.
Page 47 and 48: CHAPTER 10 REVIEW 0 39 25. x = t +
Page 49 and 50: 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,.
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SECTION 11.1 SEQUENCES D 49 71. Sin
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SECTION 11.2 SERIES 0 51 ak+l- a1.:
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SECTION 11.2 SERIES 0 53 13. n s.,
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SECTION 11.2 SERIES 0 55 47. F~r th
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. . (1+ c)- 2 scn es and set 1t equ
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SECTION 11.3 THE INTEGRAL TEST AND
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, SECTION 11.3 THE INTEGRAL TEST AN
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SECTION 11.4 THE COMPARISON TESTS D
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SECTION 11.5 ALTERNATING SERIES 0 6
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SECTION 11.5 ALTERNATING SERIES D 6
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SECTION 11.6 ABSOLUTE CONVERGENCE A
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SECTION 11.6 ABSOLUTE CONVERGENCE A
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17 lim I an+l I= SECTION 11.7 STRAT
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SECTION 11.8 POWER SERIES 0 75 l 00
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SECTION 11.8 POWER SERIES 0 n (b) I
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SECTION 11.9 REPRESENTATIONS OF FUN
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SECTION 11.9 REPRESENTATIONS OF FUN
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SECTION 11.10 TAYLOR AND MACLAURIN
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61 _ x_ x · sin x - x- tx 3 + 1~
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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 16.7 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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