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

Recommendations

Info

104 0 CHAPTER 11 INFINITE SEQUENCES AND SERIES (b) 1.5 (c) IR3 (x) l $ ~~ ix - 11 4 , where J! ( 4 ) (x) J $ M with j ( 4 >(x) = - ~~x- 7 1 2 . Now 0.9 ~ x $ 1.1 => - 0.1 ~ X- 1 ~ 0.1 => (x- 1) 4 $ ·(0.1) 4 , d I . 0 . . 15 an etting x = .9 gtves M = ( _ )7 , 16 0 9 12 so 0 2 IRa(x) l $ 16 (0. ~~ 712 41 (0.1)4 :::::: 0.000005648 :::::: 0.000 006 = 6 X lO- G (d) 5 X 10- 6 From the graph of IR3(x)l = I JX - T3(x)l. it appears that the error is less than 5 x w- 6 on [0.9, 1.1]. oo • x2n+l x3 x6 x7 . x3 xs x7 59.sin x = 2:(- 1t ( 2 1 ) 1 = x- - +---+· ··,sosmx - x=--+---+··· and n=O n + . 3! 5! 7! 3! 5! 7! 00 00 00 61. f(x ) = 2: Cn x" => f(-x)= l: cn(-xt = 2:(- 1)"c.,x" n=O n =O n=O (a) Iff is an odd function, then f( - x) = - f(x) => 00 00 2: (- 1)"cnx" = 2: - c,,x". The coefficients of any power series u=O are uniquely determined (by Theorem 11.10.5), so ( -1)" Cn = - en. If n is even, then ( - 1)" = 1, so en = -c,. => 2en = 0 => c,. = 0. Thus, all even coefficients are 0, that is, Co = C2 = C4 = · · · = 0. 00 00 (b) Iff is even, then f (-x) = f(x) => 2: {-lt c,. xn = 2: Cn x" => {-1)" Cn = Cn. n=O n = O If n is odd, then ( - 1 )" = -1, so -en = Cn => 2c,.. = 0 => Cn = 0. Thus, all odd coefficients are 0, that is, Cl = C3 = C5 = · · · = 0. n=O ' @) 2011 Ccngoge Lcorning. All Rigbls Reserved. Moy not be scanned. copied, or
D PROBLEMS PLUS 1. It would be far too much work to compute 15 derivatives of f. The key idea is to remember that j 1, Pn -> oo as n-> oo. so= 3 eo = 1 81 = 3 · 1 e1 = 1 / 3 S2 = 3 · 4 2 e2 = 1/ 3 2 S 3 = 3 · 4 3 e3 = 1/ 3 3 (c) The area of each of the small triangles added at a given stage is one-ninth of the area of the triangle added at the preceding stage. Let a. be the area of the original triangle. Then the area an of each of the small triangles added at stage n is e 2012 CcngUl_;C Lcamin&- All Rig)tts RL"SCr\'cd. Ma)' nol be scanned. copied. or duplic31Cd. or pos1l-d to a publicly accessible websile, in whole or in part. 105
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
Page 13 and 14:
SECTION 10.1 CURVES DEFINED BY PARA
Page 15 and 16:
SECTION 10.2 CALCULUS WITH PARAMETR
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
SECTION 10.3 POLAR COORDINATES 0 13
Page 23 and 24:
Page 25 and 26:
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,.
Page 57 and 58:
SECTION 11.1 SEQUENCES D 49 71. Sin
Page 59 and 60:
SECTION 11.2 SERIES 0 51 ak+l- a1.:
Page 61 and 62: SECTION 11.2 SERIES 0 53 13. n s.,
Page 63 and 64: SECTION 11.2 SERIES 0 55 47. F~r th
Page 65 and 66: . . (1+ c)- 2 scn es and set 1t equ
Page 67 and 68: SECTION 11.3 THE INTEGRAL TEST AND
Page 69 and 70: , SECTION 11.3 THE INTEGRAL TEST AN
Page 71 and 72: SECTION 11.4 THE COMPARISON TESTS D
Page 73 and 74: SECTION 11.5 ALTERNATING SERIES 0 6
Page 75 and 76: SECTION 11.5 ALTERNATING SERIES D 6
Page 77 and 78: SECTION 11.6 ABSOLUTE CONVERGENCE A
Page 79 and 80: SECTION 11.6 ABSOLUTE CONVERGENCE A
Page 81 and 82: 17 lim I an+l I= SECTION 11.7 STRAT
Page 83 and 84: SECTION 11.8 POWER SERIES 0 75 l 00
Page 85 and 86: SECTION 11.8 POWER SERIES 0 n (b) I
Page 87 and 88: SECTION 11.9 REPRESENTATIONS OF FUN
Page 89 and 90: SECTION 11.9 REPRESENTATIONS OF FUN
Page 91 and 92: SECTION 11.10 TAYLOR AND MACLAURIN
Page 97 and 98: 61 _ x_ x · sin x - x- tx 3 + 1~
Page 99 and 100: SECTION 11.11 APPLICATIONS OF TAYLO
Page 105 and 106: CHAPTER 11 REVIEW 0 97 J'(xn)(xn -
Page 107 and 108: CHAPTER 11 REVIEW 0 99 oo f (n) (O)
Page 109 and 110: CHAPTER 11 REVIEW 0 101 l 23. Consi
Page 111: 49./- 1 - dx = -ln{4- x) + C and 4-
Page 115 and 116: CHAPTER 11 PROBLEMS PLUS D 107 l 9.
Page 117 and 118: CHAPTER 11 PROBLEMS PLUS 0 109 x x
Page 119 and 120: 112 0 CHAPTER 12 VECTORS AND THE GE
Page 127 and 128: 120 D CHAPTER 12 VECTORS AND THE GE
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 and 156: l CHAPTER 12 PROBLEMS PLUS 0 149 Eq
Page 157 and 158: 13 D VECTOR FUNCTIONS 13.1 Vector F
Page 159 and 160: SECTION 13.1 VECTOR FUNCTIONS AND S
Page 161 and 162: SECTION 13.1 VECTOR FUNCTIONS AND S
Page 163 and 164:
SECTION 13.2 DERIVATIVES AND INTEGR
Page 165 and 166:
SECTION 13.2 DERIVATIVES AND INTEGR
Page 167 and 168:
SECTION 13.3 ARC LENGTH AND CURVATU
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
SECTION 13.4 MOTION IN SPACE: VELOC
Page 177 and 178:
2 SECTION 13.4 MOTION IN SPACE: VEL
Page 179 and 180:
CHAPTER 13 REVIEW D 173 43. The tan
Page 181 and 182:
5. f~(t 2 i +tcos 1rtj +sin 1rt k )
Page 183 and 184:
CHAPTER 13 REVIEW 0 177 23. (a) r (
Page 185 and 186:
180 0 CHAPTER 13 PROBLEMS PLUS (-2a
Page 187 and 188:
182 0 CHAPTER 13 PROBLEMS PLUS vect
Page 189 and 190:
184 0 CHAPTER 14 PARTIAL DERIVATIVE
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
196 D CHAPTER 14 PARTIAL DERIVATIVE
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
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
Page 255 and 256:
l SECTION 15.3 DOUBLE INTEGRALS OVE
Page 257 and 258:
SECTION 15.3 DOUBLE INTEGRALS OVER
Page 259 and 260:
SECTION 15.3 DOUBLE INTEGRALS OVER
Page 261 and 262:
61 . Since m :S j(x, y) :S M, ffD m
Page 263 and 264:
SECTION 15.4 DOUBLE INTEGRALS IN PO
Page 265 and 266:
SECTION 15.5 APPLICATIONS OF DOUBLE
Page 267 and 268:
SECTION 15.5 APPLICATIONS OF DOUBLE
Page 269 and 270:
SECTION 1505 APPLICATIONS OF DOUBLE
Page 271 and 272:
-I SECTION 15.6 SURFACE AREA 0 267
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~
Page 279 and 280:
43. I,. = foL foL foL k(y2 + z2)dz.
Page 281 and 282:
SECTION 15.8 TRIPLE INTEGRALS IN CY
Page 283 and 284:
M xv = I~1f I: I:2 6 - 3 r 2 (zK) r
Page 285 and 286:
SECTION 15.9 TRIPLE INTEGRALS IN SP
Page 287 and 288:
SECTION 15.9 TRIPLE INTEGRALS IN SP
Page 289 and 290:
(b) The wedge in question is the sh
Page 291 and 292:
SECTION 15.10 CHANGE OF VARIABLES I
Page 293 and 294:
CHAPTER 15 REVIEW 0 289 15 Review C
Page 295 and 296:
CHAPTER 15 REVIEW 0 291 l 9. The vo
Page 297 and 298:
CHAPTER 15 REVIEW D 293 33. Using t
Page 299 and 300:
49. Since u = x- y and v = x + y, x
Page 301 and 302:
298 D CHAPTER 15 PROBLEMS PLUS To e
Page 303 and 304:
300 0 CHAPTER 15 PROBLEMS PLUS 13.
Page 305 and 306:
16 0 VECTOR CALCULUS 16.1 Vector Fi
Page 307 and 308:
SECTION 16.2 LINE INTEGRALS 0 305 2
Page 309 and 310:
SECTION 16.2 LINE INTEGRALS 0 307 (
Page 311 and 312:
SECTION 16.2 LINE INTEGRALS D 309 3
Page 313 and 314:
SECTION 16.3 THE FUNDAMENTAL THEORE
Page 315 and 316:
SECTION 16.4 GREEN'S THEOREM D 313
Page 317 and 318:
SECTION 16.4 GREEN'S THEOREM 0 315
Page 319 and 320:
8 8 8 (b)clivF = 'V ·iF=- (x+yz) +
Page 321 and 322:
SECTION 16.5 CURL AND DIVERGENCE 0
Page 323 and 324:
SECTION 16.6 PARAMETRIC SURFACES AN
Page 325 and 326:
Page 327 and 328:
Page 329 and 330:
that is, D = {( x, y) I x 2 + y 2 :
Page 331 and 332:
SECTION 16.7 SURFACE INTEGRALS 0 32
Page 333 and 334:
SECTION 16.7 SURFACE INTEGRALS 0 33
Page 335 and 336:
SECTION 16.8 STOKES' THEOREM 0 333
Page 337 and 338:
dS SECTION 16.9 THE DIVERGENCE THEO
Page 339 and 340:
CHAPTER 16 REVIEW 0 337 27. JI 5 cu
Page 341 and 342:
CHAPTER 16 REVIEW 0 339 TRUE-FALSE
Page 343 and 344:
CHAPTER 16 REVIEW D 341 Alternate s
Page 345 and 346:
344 0 CHAPTER 16 PROBLEMS PLUS Simi
Page 347 and 348:
3.c6 0 CHAPTER 17 SECOND-ORDER DIFF
Page 349 and 350:
348 0 CHAPTER 17 SECOND-ORDER DIFFE
Page 351 and 352:
Page 353 and 354:
352 D CHAPTER 17 SECOND-ORDER DIFFE
Page 355 and 356:
Page 357 and 358:
356 D CHAPTER 17 SECOND-ORDER DIFFE
Page 359 and 360:
0 APPENDIX Appendix H Complex Numbe
Page 361:
APPENDIX H COMPLEX NUMBERS 0 361 43
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?