Solução_Calculo_Stewart_6e

Recommendations

Info

F. TX.10 SECTION 2.8 THEDERIVATIVEASAFUNCTION ¤ 71 (b) After 800 ounces of gold have been produced, the rate at which the production cost is increasing is $17/ounce. So the cost of producing the 800th (or 801st) ounce is about $17. (c) In the short term, the values of f 0 (x) will decrease because more efficient use is made of start-up costs as x increases. But eventually f 0 (x) might increase due to large-scale operations. 47. T 0 (10) is the rate at which the temperature is changing at 10:00 AM.ToestimatethevalueofT 0 (10), we will average the difference quotients obtained using the times t =8and t =12.LetA = B = T (12) − T (10) 12 − 10 = 88 − 81 2 T (8) − T (10) 8 − 10 = 72 − 81 −2 =4.5 and =3.5. ThenT 0 T (t) − T (10) (10) = lim ≈ A + B = 4.5+3.5 =4 ◦ F/h. t→10 t − 10 2 2 49. (a) S 0 (T ) is the rate at which the oxygen solubility changes with respect to the water temperature. Its units are (mg/L)/ ◦ C. (b) For T =16 ◦ C, it appears that the tangent line to the curve goes through the points (0, 14) and (32, 6). So S 0 (16) ≈ 6 − 14 32 − 0 = − 8 32 = −0.25 (mg/L)/◦ C. This means that as the temperature increases past 16 ◦ C, the oxygen solubility is decreasing at a rate of 0.25 (mg/L)/ ◦ C. 51. Since f(x) =x sin(1/x) when x 6= 0and f(0) = 0, wehave f 0 f(0 + h) − f(0) h sin(1/h) − 0 (0) = lim =lim =limsin(1/h). This limit does not exist since sin(1/h) takes the h→0 h h→0 h h→0 values −1 and 1 on any interval containing 0. (Compare with Example 4 in Section 2.2.) 2.8 The Derivative as a Function 1. It appears that f is an odd function, so f 0 will be an even function—that is, f 0 (−a) =f 0 (a). (a) f 0 (−3) ≈ 1.5 (b) f 0 (−2) ≈ 1 (c) f 0 (−1) ≈ 0 (d) f 0 (0) ≈−4 (e) f 0 (1) ≈ 0 (f ) f 0 (2) ≈ 1 (g) f 0 (3) ≈ 1.5 3. (a) 0 = II, since from left to right, the slopes of the tangents to graph (a) start out negative, become 0, then positive, then 0,then negative again. The actual function values in graph II follow the same pattern. (b) 0 = IV, since from left to right, the slopes of the tangents to graph (b) start out at a fixed positive quantity, then suddenly become negative, then positive again. The discontinuities in graph IV indicate sudden changes in the slopes of the tangents. (c) 0 = I, since the slopes of the tangents to graph (c) are negative for x0,asarethefunctionvaluesof graph I. (d) 0 = III, since from left to right, the slopes of the tangents to graph (d) are positive, then 0, then negative, then 0, then positive, then 0, then negative again, and the function values in graph III follow the same pattern.
F. 72 ¤ CHAPTER 2 LIMITS AND DERIVATIVES TX.10 Hints for Exercises 4 –11: First plot x-intercepts on the graph of f 0 for any horizontal tangents on the graph of f . Look for any corners on the graph of f— there will be a discontinuity on the graph of f 0 . On any interval where f has a tangent with positive (or negative) slope, the graph of f 0 will be positive (or negative). If the graph of the function is linear, the graph of f 0 will be a horizontal line. 5. 7. 9. 11. 13. It appears that there are horizontal tangents on the graph of M for t = 1963 and t = 1971. Thus, there are zeros for those values of t on the graph of M 0 . The derivative is negative for the years 1963 to 1971. 15. The slope at 0 appears to be 1 and the slope at 1 appears to be 2.7. Asx decreases, the slope gets closer to 0. Since the graphs are so similar, we might guess that f 0 (x) =e x .
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: F. TX.10 20 ¤ CHAPTER 1 FUNCTIONS
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 63: F. 70 ¤ CHAPTER 2 LIMITS AND DERIV
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 115 and 116:
F. 122 ¤ CHAPTER 3 DIFFERENTIATION
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:
Page 337 and 338:
Page 339 and 340:
Page 341 and 342:
Page 343 and 344:
F. TX.10
Page 345 and 346:
Page 347 and 348:
F. TX.10
Page 349 and 350:
F. 356 ¤ CHAPTER 8 FURTHER APPLICA
Page 351 and 352:
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
Page 375 and 376:
F. 382 ¤ CHAPTER 9 DIFFERENTIAL EQ
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
Page 383 and 384:
Page 385 and 386:
Page 387 and 388:
Page 389 and 390:
Page 391 and 392:
Page 393 and 394:
Page 395 and 396:
Page 397 and 398:
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
F. TX.10
Page 405 and 406:
F. 412 ¤ CHAPTER 10 PARAMETRIC EQU
Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
Page 413 and 414:
Page 415 and 416:
Page 417 and 418:
Page 419 and 420:
Page 421 and 422:
Page 423 and 424:
Page 425 and 426:
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
Page 437 and 438:
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?