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

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266 D CHAPTER 15 MULTIPLE INTEGRALS f(x, y) = /I(x)/2(y) = 1 e-(x-45) 2 /0.s 1 e-(y-20) 2 /0.02 = lQe - 2 (x-45) 2 -so(v -2~)2. 0.5 ..,l2ir 0.1 ..,f2ir " . Then P(40
-I SECTION 15.6 SURFACE AREA 0 267 15.6 Surface Area 1. Here z = f(x, y) = 2 + 3x + 4y and Dis the rectangle [0, 5) x [I, 4), so by Formula 2 the area of the surface is A(S) = ffD J[f,(x,y)] 2 + [! 11 (x,y)]2 + I dA= ffo -../3 2 +4 2 +IdA= ../26ffDdA = ../26 A( D) = ../26 (5)(3) = I5 ../26 3. z = f(x, y) = 6- 3x - 2y which intersects the xy-plane in the line 3x + 2y = 6, 'soD is the triangular region given by {(x,y) I 0:5 x :5 2,0:5 y :53- ~x}. Thus A(S) = JJD J( -3) 2 + ( -2) 2 +IdA= .JI4 ffo dA = JI4 A( D ) = JI4 (~ · 2 · 3) = 3 .JI4 5. y 2 + z 2 = 9 =* z = ~ · fx = 0, fv = -y(9 - y 2 ) - 112 =* A(S) = h412 Jo2 + [- y(9- y2)-1/2)2 + 1 dy dx = h4 h 2 J 9 ~2y2 + I dy dx = t { 2 3 lo lo J9 - y 2 lo · 3 v=O 7. z = f(x, y) = y 2 - x 2 with I ::; x 2 + y 2 ::; 4. Then dydx = 3 t [sin- 1 IL] 11 = 2 dx = 3 [(sin- 1 (~))x]~ = I 2sin- 1 (~) A( S) = J f D J 1 + 4x 2 + 4y 2 2 2 dA = .{ 0 2" f 1 Vf+"4r2 r dr dO = J:.,. dO J 1 r -../I + 4r2 dr = (0]~" u2(I + 4r 2 ) 3 1 2 J: = {f(17vT7 - 5v'5) 9. z = f(x, y) = xy with x 2 + y 2 :5 1, so / ex = y, f v =X =* A(S) = JJ Jy 2 + x 2 + 1dA = t" r 1 -../r 2 +I r dr dO= J; 2 " [l(1·2 + 1) 3 1 2 ] r=l dO . D 0 J o 0 3 r=O = I:'lr H2-../2 - I) dO= 2 I(2-../2 - 1) A(S) = !L x2 +y2 2 2 2+ IdA a - x - y "/2 1 acos6 / r2 = /_ --+ 1rdrd0 - 1r/2 o a2 - r2 a coso ar = drdO /_ - .r/2 o · Va 2 - r 2 'lr f21 = /_"/2 [-a Ja2...:. r2 ] r=acose dO - 1rj2 r=O 1r/2 1 -rr/2 = -a( J a2 - a 2 cos 2 0-a) dO = 2a 2 (I - Vl - cos 2 0) dO /_ -1r/2 0 ® 20 12 Cengage Looming. All Rights Reserved. May not be sc:uu>ed, copied, or duplicated, or posted too publicly occcssiblc website, in whole or in port.
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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. ~
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0 PROBLEMS PLUS l lt sin u dx cost
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11 . D INFINITE SEQUENCES AND SERIE
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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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Page 219 and 220: 214 0 CHAPTER 14 PARTIAL DERIVATIVE
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Page 249 and 250: D PROBLEMS PLUS 1. The areas of the
Page 251 and 252: 15 D MULTIPLE INTEGRALS 15.1 Double
Page 253 and 254: SECTION 15.2 ITERATED INTEGRALS D 2
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Page 257 and 258: SECTION 15.3 DOUBLE INTEGRALS OVER
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Page 261 and 262: 61 . Since m :S j(x, y) :S M, ffD m
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Page 265 and 266: SECTION 15.5 APPLICATIONS OF DOUBLE
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Page 273 and 274: SECTION 15.7 TRIPLE INTEGRALS 0 269
Page 275 and 276: SECTION 15.7 TRIPLE INTEGRALS D 271
Page 277 and 278: Therefore E = { (x, y, z) I -2 ~ X~
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Page 313 and 314: SECTION 16.3 THE FUNDAMENTAL THEORE
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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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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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