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

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14 0 CHAPTER 10 PARAMETRIC EQUATIONS AND POLAR COORDINATES (b) (1, - 3 ;) r > 0: (1, - 3 ; + 21r) = (1, 5 ;) 0 r < 0: (- 1,- 3 r+ 7r) = (-1,~) _ 311' 4 (c) ( - 1, 2J) r > 0: (- (- 1), 1J +1r) = (1, 3 ;) 0 ,. 2 r < 0: (-1, ~ + 21r) = (- 1, 5 2 ,.) (-t,f) 3. (a) X= 1COS7r = 1(- 1) = -1 and (l, 'TT) 0 'TT y = 1 sin 1r = 1(0) = 0 give us the Cartesian coordin~tes ( -1, 0). (b) x = 2cos(- 2 3 "' ) = 2(-~) = - 1 and y = 2sin( - 2 ;) = 2( - ~) ~ ~VS give us ( -1, -V3). (c) x = -2cos 3 ; = -2( -4) = J2 and y = - 2sin 3 4 " = -~( 4) = - J2 gives us ( J2, -J2). 5. (a) x = 2 andy = - 2 => r = J2 2 + (-2)2 = 2 J2 and 8 = tan- 1 ( :n := -~ . Since (2, -2) is in the fourth quadrant, the polar coordinates are (i) (2 J2, 7 ;) and (ii) (-2 J2, 3 ;). (b) x = - 1 andy = V3 => r = J< -1) 2 + ( v'3) 2 = 2 and 8 = tan~ 1 ( :1) = 2 :;. Since_( -1, VS) is in the second quadrant, the polar coordinates are (i) (2, ~)and (ii) ( - 2, 6 ;). '· © 2012 Cengnge Learning. All Rights Reserved. May no1 be scnnned, copied, or dupll
SECTION 10.3 POLAR COORDINATES 0 15 7. r ~ 1. The curve r = 1 represents a circle with center 0 and radius 1. So r ~ 1 represents the region on or outside the circle. Note that 8 can take on any value. 9. r ~ 0, 7r/4 S, B S, 37r/ 4 . . 8 = IC represents a line through 0. 0= 37T 4 0='!!.. 4 11 2 < < 3 s.,.. < B < r1r · r •a--a 0 - 11< - 3 r=2 o- s1f - 3 13. ·Converting the p~lar coordinates (2, 1r / 3) and ( 4, 21r / 3) to Cartesian coordinates gives us (2 cos f, 2 sin f) = (1, J3) and ( 4 cos 2 ; , 4 sin 2 ;) = (- 2, 2 J3). Now use the distance !ormula. 15. r 2 = 5
Page 1 and 2: - STUDENT SOLUTIONS MANUAL for STEW
Page 3 and 4: .. BROOKS/COLE ~ I ~~r CENGAGE Lear
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
Page 21: SECTION 10.3 POLAR COORDINATES 0 13
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Page 39 and 40: x2 y2 y2 a:2 _ a2 b 61. ;_2 - - = 1
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Page 43 and 44: CHAPTER 10 REVIEW 0 35 the length o
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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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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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