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

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150 0 CHAPTER 12 PROBLEMS PLUS h _ (sin0+J.£.cos8) _ · ( tan8 +J.£.) max- mg - mg cos 0 - J.£ 8 sin B 1 - J.£ 8 tan B tanB +tan B. ) == mg ( 1- tan B. tanB = mgtan(B +B .• ) We would expect hmax to increase as 8 increases, with similar behavior as we established for hmin, but with hmax values al~ays larger than hmin· We can see that this is. the case if we graph hmo.x as a function of 8, as the curve is the graph of hmin translated 20. to the left, so the equation does seem reasonable. Notice that the equation predicts hmo.x --+ oo as . 8--+ (90° - 0., ). In fact, as hmnx increases, the nonnal force increases as well. When (90° - Bs) :50 :S: 90°, the horizontal force is completely counteracted by the sum of the f!Orlnal and frictional forces, so no part of the horizontal force contributes to moving the block up the plane no matter how large its magnitude: ® 2012 Cen&ns• Lc3tning. All Rights Rescn·ed. May not be SCMn
13 D VECTOR FUNCTIONS 13.1 Vector Functions and Space Curves 1. The component functions v'4- t 2 , e- 3 t, and ln(t + 1) are a ll defined wher4 - t 2 2: 0 => - 2 ~ t ~ 2 and t + 1 > 0 => t > - 1, so the domain ofr is ( -1, 2]. 1 1 - = t-+O t--+o sin 2 t . t.-o sin 2 t lim sin 2 t ~ t--+0 t2 3. lim e- 31 = e 0 = 1, lim~= lim - and lim cos 2t = cos 0 = 1. Thus t-+0 = 1 _ I_ _ 1 . t)2 - !2 - ' ( lim~ t --+0 t lim (e-st i + 4 j +cos 2t k) = [lim e- 3 t] i + [urn 4] j + [rim cos 2t] k = i + j + k. t-+O sm t t-+O t-+O sm t t -+O ] . 1 + t 2 1 . (1/ t2 ) + 1 0 + 1 1 1 . _ 1 t ,. 1 . 1 - e-2 t S. ~~ 1- t2 1 . 1 1 = t~ (1/t2)- 1 = 0 - 1 = - 't 2.~ tan = 2 • t~ t = t2.~ t - -te_2_t = 0 - 0 = 0· Thus ( 1 + e 1 - e- 2 t) . lim - 1 2 ,tan-1 t, t =(-l,f,O). t--+oo - t 7. The corresponding parametric equations for this curve are x = sin t, y = t. We can make a table of values, or we can eliminate the parameter: t = y => x = sin y, with y E JR. By comparing different values oft, we find tl)e direction in which t increases as indicated in the graph. X 9. The corresponding parametric equations are x = t, y = 2 - t, z = 2t, which are parametric equations of a line through the point (0, 2, 0) and with direction vector (1, -1, 2). ® 2012 Cengagc Leamins. All Rights Rcxrvcd. Mny not be scanned, copied, or duplicnted, or posted too publicly IICtcs.•lble website, in whole or in pm. 151
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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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Page 105 and 106: CHAPTER 11 REVIEW 0 97 J'(xn)(xn -
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Page 113 and 114: D PROBLEMS PLUS 1. It would be far
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Page 117 and 118: CHAPTER 11 PROBLEMS PLUS 0 109 x x
Page 119 and 120: 112 0 CHAPTER 12 VECTORS AND THE GE
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Page 143 and 144: 136 D CHA~TER 12 VECTORS AND THE GE
Page 153 and 154: D PROBLEMS PLUS 1. Since three-dime
Page 155: l CHAPTER 12 PROBLEMS PLUS 0 149 Eq
Page 159 and 160: SECTION 13.1 VECTOR FUNCTIONS AND S
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Page 163 and 164: SECTION 13.2 DERIVATIVES AND INTEGR
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Page 167 and 168: SECTION 13.3 ARC LENGTH AND CURVATU
Page 175 and 176: SECTION 13.4 MOTION IN SPACE: VELOC
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Page 179 and 180: CHAPTER 13 REVIEW D 173 43. The tan
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Page 185 and 186: 180 0 CHAPTER 13 PROBLEMS PLUS (-2a
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202 0 CHAPTER 14 PARTIAL DERIVATIVE
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204 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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