Solução_Calculo_Stewart_6e

Recommendations

Info

F. TX.10 SECTION 9.4 MODELS FOR POPULATION GROWTH ¤ 393 (b) Using the logistic equation (4), dP 1 dt = kP − P , we substitute y = P dP , P = Ky,and K K dt = K dy dt , to obtain K dy dt dy = k(Ky)(1 − y) ⇔ = ky(1 − y), our equation in part (a). dt Now the solution to (4) is P (t) = We use the same substitution to obtain Ky = K K − P0 ,whereA = . 1+Ae−kt P 0 K y 0 1+ K − ⇒ y = Ky0 e Ky −kt y 0 +(1− y 0 )e . −kt 0 Alternatively, we could use the same steps as outlined in the solution of Equation 4. (c) Let t be the number of hours since 8 AM. Theny 0 = y(0) = 80 1000 =0.08 and y(4) = 1 2 ,so 1 2 = y(4) = 0.08 0.08 + 0.92e −4k . Thus, 0.08 + 0.92e−4k =0.16, e −4k = 0.08 0.92 = 2 23 ,ande−k = 2 23 1/4 , so y = 0.08 0.08 + 0.92(2/23) = 2 . Solving this equation for t,weget t/4 t/4 2 + 23(2/23) t/4 2 ⇒ = 2 − 2y t/4 2 ⇒ = 2 23 23y 23 23 · 1 − y y t/4 2 2y +23y =2 23 It follows that t 4 When y =0.9, 1 − y y the rumor by 3:36 PM. 9. (a) dP 1 dt = kP − P K ln[(1 − y)/y] − 1= ln 2 ,sot =4 23 = 1 9 ,sot =4 1 − ln 9 ln 2 23 ⇒ d2 P dt 2 1+ = k P − 1 K = k kP 1 − P K ln((1 − y)/y) ln 2 23 . ⇒ 2 23 t/4−1 = 1 − y . y ≈ 7.6 hor7 h 36 min. Thus, 90% of the population will have heard dP + 1 − P dt K dP = k dP dt dt 1 − P K 1 − 2P = k 2 P K − P K +1− P K 1 − 2P K (b) P grows fastest when P 0 has a maximum, that is, when P 00 =0. From part (a), P 00 =0 ⇔ P =0, P = K, or P = K/2. Since0
F. 394 ¤ CHAPTER 9 DIFFERENTIAL EQUATIONS TX.10 (b) Since k>0, there will be an exponential expansion ⇔ P 0 − m k > 0 ⇔ mkP0. (d) P 0 =8,000,000, k = α − β =0.016, m = 210,000 ⇒ m>kP 0 (= 128,000), so by part (c), the population was declining. 15. (a) The term −15 represents a harvesting of fish at a constant rate—in this case, 15 fish/week. This is the rate at which fish are caught. (b) (c) From the graph in part (b), it appears that P (t) = 250 and P (t) =750 are the equilibrium solutions. We confirm this analytically by solving the equation dP/dt =0as follows: 0.08P (1 − P/1000) − 15 = 0 ⇒ 0.08P − 0.00008P 2 − 15 = 0 ⇒ −0.00008(P 2 − 1000P + 187,500) = 0 ⇒ (P − 250)(P − 750) = 0 ⇒ P = 250 or 750. (d) For 0
Page 1 and 2:
F. TX.10 Solução detalhada de tod
Page 3 and 4:
F. TX.10 10 ¤ CHAPTER 1 FUNCTIONS
Page 5 and 6:
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
F. TX.10
Page 33 and 34:
F. TX.10 40 ¤ CHAPTER 1 PRINCIPLES
Page 35 and 36:
F. 42 ¤ CHAPTER 2 LIMITS AND DERIV
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
F. TX.10
Page 79 and 80:
F. 86 ¤ CHAPTER 2 PROBLEMS PLUS TX
Page 81 and 82:
F. 88 ¤ CHAPTER 3 DIFFERENTIATION
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
F. TX.10
Page 133 and 134:
F. 140 ¤ CHAPTER 3 PROBLEMS PLUS T
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
F. TX.10
Page 141 and 142:
F. 148 ¤ CHAPTER 4 APPLICATIONS OF
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
F. TX.10 202 ¤ CHAPTER 4 APPLICATI
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
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:
F. TX.10
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
F. TX.10
Page 227 and 228:
F. 234 ¤ CHAPTER 5 INTEGRALS 3.
Page 229 and 230:
F. 236 ¤ CHAPTER 5 INTEGRALS TX.10
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:
Page 251 and 252:
Page 253 and 254:
F. TX.10
Page 255 and 256:
F. 262 ¤ PROBLEMS PLUS TX.10 (b) W
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
F. TX.10
Page 285 and 286:
F. 292 ¤ CHAPTER 6 PROBLEMS PLUS (
Page 287 and 288:
F. TX.10
Page 289 and 290:
F. 296 ¤ CHAPTER 7 TECHNIQUES OF I
Page 291 and 292:
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
Page 309 and 310:
Page 311 and 312:
Page 313 and 314:
Page 315 and 316:
Page 317 and 318:
Page 319 and 320:
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
Page 329 and 330:
F. TX.10 336 ¤ CHAPTER 7 TECHNIQUE
Page 331 and 332:
Page 333 and 334:
Page 335 and 336: F. 342 ¤ CHAPTER 7 TECHNIQUES OF I
Page 343 and 344: F. TX.10
Page 345 and 346: F. 352 ¤ CHAPTER 7 PROBLEMS PLUS T
Page 347 and 348: F. TX.10
Page 349 and 350: F. 356 ¤ CHAPTER 8 FURTHER APPLICA
Page 375 and 376: F. 382 ¤ CHAPTER 9 DIFFERENTIAL EQ
Page 385: F. 392 ¤ CHAPTER 9 DIFFERENTIAL EQ
Page 403 and 404: F. TX.10
Page 405 and 406: F. 412 ¤ CHAPTER 10 PARAMETRIC EQU
Page 437 and 438:
F. 444 ¤ CHAPTER 10 PARAMETRIC EQU
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
Page 445 and 446:
F. TX.10
Page 447 and 448:
F. 454 ¤ CHAPTER 10 PROBLEMS PLUS
Page 449 and 450:
F. 456 ¤ CHAPTER 11 INFINITE SEQUE
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
Page 459 and 460:
Page 461 and 462:
Page 463 and 464:
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
Page 473 and 474:
Page 475 and 476:
Page 477 and 478:
Page 479 and 480:
Page 481 and 482:
Page 483 and 484:
Page 485 and 486:
Page 487 and 488:
Page 489 and 490:
Page 491 and 492:
Page 493 and 494:
Page 495 and 496:
Page 497 and 498:
Page 499 and 500:
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
Page 507 and 508:
F. TX.10
Page 509 and 510:
F. 106 ¤ CHAPTER 13 VECTORSANDTHEG
Page 511 and 512:
Page 513 and 514:
Page 515 and 516:
Page 517 and 518:
Page 519 and 520:
Page 521 and 522:
Page 523 and 524:
Page 525 and 526:
Page 527 and 528:
Page 529 and 530:
Page 531 and 532:
Page 533 and 534:
Page 535 and 536:
Page 537 and 538:
Page 539 and 540:
F. 136 ¤ PROBLEMS PLUS TX.10 5. (a
Page 541 and 542:
F. TX.10
Page 543 and 544:
F. 140 ¤ CHAPTER 14 VECTOR FUNCTIO
Page 545 and 546:
Page 547 and 548:
Page 549 and 550:
Page 551 and 552:
Page 553 and 554:
Page 555 and 556:
Page 557 and 558:
Page 559 and 560:
Page 561 and 562:
Page 563 and 564:
Page 565 and 566:
F. 162 ¤ PROBLEMS PLUS TX.10 Now l
Page 567 and 568:
F. TX.10
Page 569 and 570:
F. 166 ¤ CHAPTER 15 PARTIAL DERIVA
Page 571 and 572:
Page 573 and 574:
Page 575 and 576:
Page 577 and 578:
Page 579 and 580:
Page 581 and 582:
Page 583 and 584:
Page 585 and 586:
Page 587 and 588:
Page 589 and 590:
Page 591 and 592:
Page 593 and 594:
Page 595 and 596:
Page 597 and 598:
Page 599 and 600:
Page 601 and 602:
Page 603 and 604:
Page 605 and 606:
Page 607 and 608:
Page 609 and 610:
Page 611 and 612:
Page 613 and 614:
Page 615 and 616:
Page 617 and 618:
Page 619 and 620:
Page 621 and 622:
Page 623 and 624:
F. TX.10
Page 625 and 626:
F. 222 ¤ PROBLEMS PLUS TX.10 Since
Page 627 and 628:
F. 224 ¤ CHAPTER 16 MULTIPLE INTEG
Page 629 and 630:
Page 631 and 632:
Page 633 and 634:
Page 635 and 636:
Page 637 and 638:
Page 639 and 640:
Page 641 and 642:
Page 643 and 644:
Page 645 and 646:
Page 647 and 648:
Page 649 and 650:
Page 651 and 652:
Page 653 and 654:
Page 655 and 656:
Page 657 and 658:
Page 659 and 660:
Page 661 and 662:
Page 663 and 664:
Page 665 and 666:
Page 667 and 668:
F. TX.10
Page 669 and 670:
F. 266 ¤ PROBLEMS PLUS TX.10 a 7 =
Page 671 and 672:
F. TX.10
Page 673 and 674:
F. 270 ¤ CHAPTER 17 VECTOR CALCULU
Page 675 and 676:
F. Then C xy dx +(x − y) dy = C
Page 677 and 678:
Page 679 and 680:
Page 681 and 682:
Page 683 and 684:
Page 685 and 686:
Page 687 and 688:
Page 689 and 690:
Page 691 and 692:
Page 693 and 694:
Page 695 and 696:
Page 697 and 698:
Page 699 and 700:
Page 701 and 702:
Page 703 and 704:
Page 705 and 706:
Page 707 and 708:
Page 709 and 710:
F. TX.10
Page 711 and 712:
F. 308 ¤ PROBLEMS PLUS TX.10 ∂
Page 713 and 714:
F. 310 ¤ CHAPTER 18 SECOND-ORDER D
Page 715 and 716:
Page 717 and 718:
Page 719 and 720:
Page 721 and 722:
Page 723:
show all

Solução_Calculo_Stewart_6e

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

Delete template?

Save as template?