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

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CHAPTER 13 PROBLEMS PLUS 0 181 The projectile hits the ground when (v sina)t- ~gt 2 = 0 => t = 2 ; sin a, so the distance traveled by the projectile is (2v/g)sin o 1 (211/g)sin L(a) = lv(t)l dt = .9 1 0 0 v ) 2 v2 ( t - - sin a + 2 cos 2 a dt .9 9 t - (v /g) sino =g 2 [ + [(vl g) cosa]2 ln (t-~sino + 2 g [using Formula 2 I in the Table of lntegrals] g = [v. 2 (~.rna)' + (~ -gsma oo.o )' + (~'"'")' m ( ~ •ina+ (~ •mo)' + (~=a Y) +~sin o g (~ •ina )' + (~=o )'- (~oooo )' m( -~•ina+ (~•ina )' + (~=o Y)] 2 = g_ [~sino · ~+ v cos 2 2 a ln(~ sino+~) +~ sino·~ - v cos 2 a ln(- ~ sino+~)] 2 g g g2 g g g g g2 g g v 2 . + v 2 2 1n( (vl g)sina+v/g) v 2 . + v 2 2 1 (1+sino) = - stno -cos a = -sma -cos an g 2f1 - (vI g) sin a +vI g g 2g 1 - sin a We want to maximize L( a) for 0 s; a s; 1r / 2. v 2 v 2 [ 2 1 - sin a 2 cos a . ( 1 + sin a)] L'(a) =-coso+ - cos a · . · . 2 1 2 - 2cosa smo ln . g g +sma (1-smo) . 1 -sm o v 2 • v 2 [ = - cos a + - cos 2 . ( 1 + sin 2 a)] 2 a ·-- - 2 cos a sm a ln . g g coso , 1 -sma v 2 v 2 [ • (l+sina)] v 2 . = - COSO! [ 2- SIDQ . • ln (1+ sina . ) ] 9 g 1 -SlDO! 9 1 -SJDO! , = - COSO!+- COSO! 1-SlDO! ln L( a ) has critical points for 0 < a < 1r 12 when L' (a) = 0 => 2 - sin a ln ( ~ + s~ a) = 0 [since cos a =1= 0]. - SIDQ Solving by graphing (or using a CAS) gives a~ 0.9855. Compare values at the critical point and the endpoints: L(O) = 0, L( 1r 12) = v 2 I g, and £(0.9855) ~ 1.20v 2 I g. Thus the distance traveled by the projectile is maximized for a ~ 0.9855 or ~ 56°. 7. We can write the vector equation as r (t) = ·at 2 + bt + c where a= (a1, a2, a a}, b = (b1 , b2 , ba }, and c = (c1, c2, c3). Then r ' (t) = 2t a+ b which says that each tangent vector is the sum of a scalar multiple of a and the vector b . Thus the tangent vectors are all parallel to the plane determined by a and b so the curve must be parallel to this plane. [Here we assume that a and bare nonparallel. Otherwise the tangent vectors are all parallel and the curve lies along a single line.] A normal © 2012 Ccngoge Lcoming. All RighLS Rescm :d. May oot be scanocd, copied, 0< duplicnted. 0< poSied to a publicly :10e
182 0 CHAPTER 13 PROBLEMS PLUS vector for the plane is a x b = (a2b3- a3~, a3b1 - a1b3, a1b2 - a2b1). The point (c1. c2, c3) lies on the plane (when t = 0), so an equation of the plane is or (a2b3- a31h)(x- c1) + (a3b1 - a 1 ~)(y - c2) + (a l~ - a2bl)(z - c3) = 0 © 2012 Cengoge Learning. All Rights Reserved. May nol be sconncd, copied, or duplicated, or posted ton pub licly accessible wcbsilc, in whole or in p.vt.
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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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232 D CHAPTER 14 PARTIAL DERIVATIVE
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234 0 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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