Thomas Calculus 13th [Solutions]

Recommendations

Info

Section 14.4 The Chain Rule 1003 18. w w u w v x u x v x w w u w v y u y v y 19. z z x z y t x t y t z z x z y s x s y s 20. y dy u r du r 21. w dw u s du s w dw u t du t 22. w w x w y w z w v p x p y p z p v p 23. w w dx w dy w dx dy since 0 r x dr y dr x dr dr w w dx w dy w dy since dx 0 s x ds y ds y ds ds Copyright 2014 Pearson Education, Inc.
Page 7:
1 Functions 1 TABLE OF CONTENTS 1.1
Page 11:
8.3 Trigonometric Integrals 569 8.4
Page 17:
2 Chapter 1 Functions 15. The domai
Page 21:
4 Chapter 1 Functions 3 0 0 ( 1) 1
Page 25:
6 Chapter 1 Functions 43. Symmetric
Page 29:
8 Chapter 1 Functions 68. (a) From
Page 33:
10 Chapter 1 Functions The complete
Page 37:
12 Chapter 1 Functions 35. 36. 37.
Page 41:
14 Chapter 1 Functions (c) domain:
Page 45:
16 Chapter 1 Functions 69. 3 y f (
Page 49:
18 Chapter 1 Functions (c) (d) 80.
Page 53:
20 Chapter 1 Functions 21. 22. peri
Page 57:
22 Chapter 1 Functions 40. sin(2 x)
Page 61:
24 Chapter 1 Functions 65. A 2, B 2
Page 65:
26 Chapter 1 Functions 1.4 GRAPHING
Page 69:
28 Chapter 1 Functions 17. [ 5, 1]
Page 73:
30 Chapter 1 Functions 35. 36. 37.
Page 77:
32 Chapter 1 Functions 9. 10. 11. 2
Page 81:
34 Chapter 1 Functions 35. After t
Page 85:
36 Chapter 1 Functions 24. Step 1:
Page 89:
38 Chapter 1 Functions y 1 36. y =
Page 93:
40 Chapter 1 Functions 56. (a) (b)
Page 97:
42 Chapter 1 Functions 1 50 50 50 (
Page 101:
44 Chapter 1 Functions 10. 5 3 5 y(
Page 105:
46 Chapter 1 Functions 37. (a) ( f
Page 109:
48 Chapter 1 Functions 50. (a) Shif
Page 113:
50 Chapter 1 Functions 65. Let h he
Page 117:
52 Chapter 1 Functions 81. (a) No (
Page 121:
54 Chapter 1 Functions 11. If f is
Page 125:
56 Chapter 1 Functions 21. (a) y =
Page 129:
58 Chapter 1 Functions Copyright 20
Page 133:
60 Chapter 2 Limits and Continuity
Page 137:
Page 141:
Page 145:
Page 149:
Page 153:
Page 157:
Page 161:
Page 165:
Page 169:
Page 173:
Page 177:
Page 181:
Page 185:
Page 189:
Page 193:
Page 197:
Page 201:
Page 205:
Page 209:
Page 213:
Page 217:
Page 221:
Page 225:
Page 229:
Page 233:
Page 237:
Page 241:
Page 245:
116 Chapter 3 Derivatives 9. m 3 3
Page 249:
118 Chapter 3 Derivatives 32. (2 )
Page 253:
120 Chapter 3 Derivatives 45. (a) T
Page 257:
122 Chapter 3 Derivatives 2. 2 2 F(
Page 261:
124 Chapter 3 Derivatives 18. 19. (
Page 265:
126 Chapter 3 Derivatives (b) The t
Page 269:
128 Chapter 3 Derivatives 48. (a) f
Page 273:
130 Chapter 3 Derivatives 59. The g
Page 277:
132 Chapter 3 Derivatives 6. y 3 2
Page 281:
134 Chapter 3 Derivatives 33. 34. 3
Page 285:
136 Chapter 3 Derivatives 56. (a) 3
Page 289:
138 Chapter 3 Derivatives 74. (a) W
Page 293:
140 Chapter 3 Derivatives 10 . (a)
Page 297:
142 Chapter 3 Derivatives 25. 6 4 3
Page 301:
144 Chapter 3 Derivatives 36. (a) v
Page 305:
146 Chapter 3 Derivatives 25. r sec
Page 309:
148 Chapter 3 Derivatives 44. We wa
Page 313:
150 Chapter 3 Derivatives 64. cos(
Page 317:
152 Chapter 3 Derivatives 3.6 THE C
Page 321:
154 Chapter 3 Derivatives y 1 6 1 1
Page 325:
156 Chapter 3 Derivatives 58. sin(
Page 329:
158 Chapter 3 Derivatives 82. g( x)
Page 333:
160 Chapter 3 Derivatives (b) y sin
Page 337:
162 Chapter 3 Derivatives (c) df dt
Page 341:
Page 345:
Page 349:
168 Chapter 3 Derivatives 47. 2 2 x
Page 353:
170 Chapter 3 Derivatives Mathemati
Page 357:
172 Chapter 3 Derivatives 13. y 2 l
Page 361:
174 Chapter 3 Derivatives 44. 1 1/2
Page 365:
Page 369:
178 Chapter 3 Derivatives 100. Supp
Page 373:
180 Chapter 3 Derivatives 3.9 INVER
Page 377:
Page 381:
184 Chapter 3 Derivatives 60. (a) D
Page 385:
186 Chapter 3 Derivatives 65. The v
Page 389:
188 Chapter 3 Derivatives 2 2 2 2 2
Page 393:
190 Chapter 3 Derivatives 35. 1 dy
Page 397:
192 Chapter 3 Derivatives 3.11 LINE
Page 401:
194 Chapter 3 Derivatives x x x x 3
Page 405:
196 Chapter 3 Derivatives 2 dA dt d
Page 409:
198 Chapter 3 Derivatives As one zo
Page 413:
200 Chapter 3 Derivatives 12. y 1 2
Page 417:
202 Chapter 3 Derivatives 43. 1 4x
Page 421:
204 Chapter 3 Derivatives 72. 2 1/2
Page 425:
206 Chapter 3 Derivatives 90. 2 t 2
Page 429:
208 Chapter 3 Derivatives 104. y si
Page 433:
210 Chapter 3 Derivatives 124. rabb
Page 437:
212 Chapter 3 Derivatives 147. Give
Page 441:
214 Chapter 3 Derivatives CHAPTER 3
Page 445:
216 Chapter 3 Derivatives 2 (b) On
Page 449:
218 Chapter 3 Derivatives k k k k d
Page 453:
220 Chapter 4 Applications of Deriv
Page 457:
Page 461:
Page 465:
Page 469:
Page 473:
Page 477:
Page 481:
Page 485:
Page 489:
Page 493:
Page 497:
Page 501:
Page 505:
Page 509:
Page 513:
Page 517:
Page 521:
Page 525:
Page 529:
Page 533:
Page 537:
Page 541:
Page 545:
Page 549:
Page 553:
Page 557:
Page 561:
Page 565:
Page 569:
Page 573:
Page 577:
Page 581:
Page 585:
Page 589:
Page 593:
Page 597:
Page 601:
Page 605:
Page 609:
Page 613:
Page 617:
Page 621:
Page 625:
Page 629:
Page 633:
Page 637:
Page 641:
Page 645:
Page 649:
Page 653:
Page 657:
Page 661:
Page 665:
Page 669:
Page 673:
Page 677:
Page 681:
Page 685:
Page 689:
Page 693:
Page 697:
Page 701:
344 Chapter 5 Integration 3. f ( x
Page 705:
346 Chapter 5 Integration 13. (a) B
Page 709:
348 Chapter 5 Integration for n in
Page 713:
350 Chapter 5 Integration n n 17. (
Page 717:
352 Chapter 5 Integration 34. (a) (
Page 721:
354 Chapter 5 Integration 45. 3 f (
Page 725:
356 Chapter 5 Integration 2 2 17. T
Page 729:
358 Chapter 5 Integration 33. 3 3 3
Page 733:
360 Chapter 5 Integration b b 54. L
Page 737:
362 Chapter 5 Integration 62. (a) 1
Page 741:
364 Chapter 5 Integration 3 1 2 1 n
Page 745:
366 Chapter 5 Integration (c) av( f
Page 749:
368 Chapter 5 Integration 95-102. E
Page 753:
370 Chapter 5 Integration 10. (1 co
Page 757:
372 Chapter 5 Integration 34. 0 x 1
Page 761:
374 Chapter 5 Integration 57. 2 x 2
Page 765:
376 Chapter 5 Integration 71. Area
Page 769:
378 Chapter 5 Integration 85 88. Ex
Page 773:
380 Chapter 5 Integration 2 1 2 2 4
Page 777:
382 Chapter 5 Integration 3 2 2 27.
Page 781:
384 Chapter 5 Integration x 53. Let
Page 785:
386 Chapter 5 Integration 72. csc x
Page 789:
388 Chapter 5 Integration (b) Use t
Page 793:
390 Chapter 5 Integration 17. Let u
Page 797:
Page 801:
394 Chapter 5 Integration 2 3 54. F
Page 805:
396 Chapter 5 Integration 65. a 0,
Page 809:
398 Chapter 5 Integration 73. Limit
Page 813:
400 Chapter 5 Integration 2 4 81. L
Page 817:
402 Chapter 5 Integration 91. c 0,
Page 821:
404 Chapter 5 Integration (c) 2 c f
Page 825:
406 Chapter 5 Integration 116. Let
Page 829:
408 Chapter 5 Integration 3. (a) (b
Page 833:
410 Chapter 5 Integration 15. f ( x
Page 837:
412 Chapter 5 Integration 27. f ( y
Page 841:
Page 845:
416 Chapter 5 Integration 68. dx du
Page 849:
418 Chapter 5 Integration 90. 3 /4
Page 853:
420 Chapter 5 Integration 110. 8 8
Page 857:
422 Chapter 5 Integration 130. The
Page 861:
424 Chapter 5 Integration 8. The de
Page 865:
426 Chapter 5 Integration 3 24. Let
Page 869:
428 Chapter 5 Integration 36. y 3 x
Page 873:
430 Chapter 5 Integration Copyright
Page 877:
432 Chapter 6 Applications of Defin
Page 881:
Page 885:
Page 889:
Page 893:
Page 897:
Page 901:
Page 905:
Page 909:
Page 913:
Page 917:
Page 921:
Page 925:
Page 929:
Page 933:
Page 937:
Page 941:
Page 945:
Page 949:
Page 953:
Page 957:
Page 961:
Page 965:
Page 969:
Page 973:
Page 977:
Page 981:
Page 985:
Page 989:
Page 993:
Page 997:
Page 1001:
Page 1005:
Page 1009:
Page 1013:
Page 1017:
Page 1021:
Page 1025:
Page 1029:
508 Chapter 7 Integrals and Transce
Page 1033:
Page 1037:
Page 1041:
Page 1045:
Page 1049:
Page 1053:
Page 1057:
Page 1061:
Page 1065:
Page 1069:
Page 1073:
Page 1077:
Page 1081:
Page 1085:
536 Chapter 7 Transcendental Functi
Page 1089:
Page 1093:
Page 1097:
Page 1101:
544 Chapter 8 Techniques of Integra
Page 1105:
Page 1109:
Page 1113:
Page 1117:
Page 1121:
Page 1125:
Page 1129:
Page 1133:
Page 1137:
Page 1141:
Page 1145:
Page 1149:
Page 1153:
Page 1157:
Page 1161:
Page 1165:
Page 1169:
Page 1173:
Page 1177:
Page 1181:
Page 1185:
Page 1189:
Page 1193:
Page 1197:
Page 1201:
Page 1205:
Page 1209:
Page 1213:
Page 1217:
Page 1221:
Page 1225:
Page 1229:
Page 1233:
Page 1237:
Page 1241:
Page 1245:
Page 1249:
Page 1253:
Page 1257:
Page 1261:
Page 1265:
Page 1269:
Page 1273:
Page 1277:
Page 1281:
Page 1285:
Page 1289:
Page 1293:
Page 1297:
Page 1301:
Page 1305:
Page 1309:
Page 1313:
Page 1317:
Page 1321:
Page 1325:
Page 1329:
Page 1333:
Page 1337:
662 Chapter 9 First-Order Different
Page 1341:
Page 1345:
Page 1349:
Page 1353:
Page 1357:
Page 1361:
Page 1365:
Page 1369:
Page 1373:
Page 1377:
Page 1381:
Page 1385:
Page 1389:
Page 1393:
Page 1397:
Page 1401:
Page 1405:
Page 1409:
Page 1413:
Page 1417:
702 Chapter 10 Infinite Sequences a
Page 1421:
Page 1425:
Page 1429:
Page 1433:
Page 1437:
Page 1441:
Page 1445:
Page 1449:
Page 1453:
Page 1457:
Page 1461:
Page 1465:
Page 1469:
Page 1473:
Page 1477:
Page 1481:
Page 1485:
Page 1489:
Page 1493:
Page 1497:
Page 1501:
Page 1505:
Page 1509:
Page 1513:
Page 1517:
Page 1521:
Page 1525:
Page 1529:
Page 1533:
Page 1537:
Page 1541:
Page 1545:
Page 1549:
Page 1553:
Page 1557:
Page 1561:
Page 1565:
Page 1569:
Page 1573:
Page 1577:
Page 1581:
Page 1585:
Page 1589:
Page 1593:
Page 1597:
Page 1601:
Page 1605:
Page 1609:
Page 1613:
Page 1617:
802 Chapter 11 Parametric Equations
Page 1621:
Page 1625:
Page 1629:
Page 1633:
Page 1637:
Page 1641:
Page 1645:
Page 1649:
Page 1653:
Page 1657:
Page 1661:
Page 1665:
Page 1669:
Page 1673:
Page 1677:
Page 1681:
Page 1685:
Page 1689:
Page 1693:
Page 1697:
Page 1701:
Page 1705:
Page 1709:
Page 1713:
Page 1717:
Page 1721:
Page 1725:
Page 1729:
Page 1733:
Page 1737:
Page 1741:
Page 1745:
Page 1749:
Page 1753:
Page 1757:
Page 1761:
Page 1765:
Page 1769:
878 Chapter 12 Vectors and the Geom
Page 1773:
Page 1777:
Page 1781:
Page 1785:
Page 1789:
Page 1793:
Page 1797:
Page 1801:
Page 1805:
Page 1809:
Page 1813:
Page 1817:
Page 1821:
Page 1825:
Page 1829:
Page 1833:
Page 1837:
Page 1841:
Page 1845:
Page 1849:
Page 1853:
Page 1857:
Page 1861:
Page 1865:
Page 1869:
928 Chapter 13 Vector-Valued Functi
Page 1873:
Page 1877:
Page 1881:
Page 1885:
Page 1889:
Page 1893:
Page 1897:
Page 1901:
Page 1905:
Page 1909:
Page 1913:
Page 1917:
Page 1921:
Page 1925:
Page 1929:
Page 1933:
Page 1937:
Page 1941:
Page 1945:
Page 1949:
Page 1953:
Page 1957:
Page 1961:
974 Chapter 14 Partial Derivatives
Page 1965:
976 Chapter 14 Partial Derivatives
Page 1969: 978 Chapter 14 Partial Derivatives
Page 2023: Section 14.4 The Chain Rule 1005 y
Page 2027: Section 14.4 The Chain Rule 1007 46
Page 2031: Section 14.5 Directional Derivative
Page 2043: Section 14.6 Tangent Planes and Dif
Page 2063: Section 14.7 Extreme Values and Sad
Page 2067: Section 14.7 Extreme Values and Sad
Page 2071:
2 33. (i) On OA, f ( x, y) f (0, y)
Page 2075:
38. (i) On OA, f ( x, y) f (0, y) 2
Page 2079:
Section 14.7 Extreme Values and Sad
Page 2083:
Page 2087:
Page 2091:
Page 2095:
5. We optimize Section 14.8 Lagrang
Page 2099:
15. T (8x 4 y) i ( 4x 2 y) j and Se
Page 2103:
Section 14.8 Lagrange Multipliers 1
Page 2107:
34. Q( p, q, r) 2( pq pr qr ) and G
Page 2111:
Section 14.8 Lagrange Multipliers 1
Page 2115:
49-54. Example CAS commands: Maple:
Page 2119:
Section 14.9 Taylors Formula for Tw
Page 2123:
Section 14.10 Partial Derivatives w
Page 2127:
Section 14.10 Partial Derivatives w
Page 2131:
Chapter 14 Practice Exercises 1059
Page 2135:
Page 2139:
Page 2143:
Page 2147:
Page 2151:
74. (i) On OA, 2 f ( x, y) f (0, y)
Page 2155:
(iii) On CD, 3 f ( x, y) f (1, y) y
Page 2159:
Page 2163:
96. Let Chapter 14 Practice Exercis
Page 2167:
Chapter 14 Additional and Advanced
Page 2171:
Page 2175:
21. (a) k is a vector normal to wil
Page 2179:
CHAPTER 15 MULTIPLE INTEGRALS 15.1
Page 2183:
Section 15.1 Double and Iterated In
Page 2187:
7. 8. Section 15.2 Double Integrals
Page 2191:
Section 15.2 Double Integrals Over
Page 2195:
Page 2199:
Page 2203:
Page 2207:
Page 2211:
Page 2215:
Section 15.3 Area by Double Integra
Page 2219:
Section 15.3 Area by Double Integra
Page 2223:
Section 15.4 Double Integrals in Po
Page 2227:
Page 2231:
Page 2235:
Page 2239:
6. The projection of D onto the xy
Page 2243:
Section 15.5 Triple Integrals in Re
Page 2247:
Section 15.5 Triple Integrals in Re
Page 2251:
Section 15.6 Moments and Centers of
Page 2255:
Page 2259:
Page 2263:
Section 15.7 Triple Integrals in Cy
Page 2267:
Page 2271:
Page 2275:
66. average 1 2 3 Section 15.7 Trip
Page 2279:
Page 2283:
Section 15.8 Substitutions in Multi
Page 2287:
Page 2291:
Page 2295:
Page 2299:
Page 2303:
Page 2307:
Page 2311:
53. x u y and y v x u v and y v 1 1
Page 2315:
Page 2319:
Page 2323:
CHAPTER 16 INTEGRALS AND VECTOR FIE
Page 2327:
Section 16.1 Line Integrals 1157 1
Page 2331:
Section 16.1 Line Integrals 1159 34
Page 2335:
Section 16.2 Vector Fields and Line
Page 2339:
(b) Section 16.2 Vector Fields and
Page 2343:
Page 2347:
Page 2351:
Page 2355:
Page 2359:
11. 2 2 Section 16.3 Path Independe
Page 2363:
Section 16.3 Path Independence, Pot
Page 2367:
Section 16.3 Path Independence, Pot
Page 2371:
Section 16.4 Greens Theorem in the
Page 2375:
Page 2379:
Page 2383:
Section 16.5 Surfaces and Area 1185
Page 2387:
(b) In a fashion similar to cylindr
Page 2391:
Page 2395:
Page 2399:
Page 2403:
Page 2407:
Section 16.6 Surface Integrals 1197
Page 2411:
Page 2415:
Page 2419:
Page 2423:
Page 2427:
Section 16.7 Stokes Theorem 1207 i
Page 2431:
Section 16.7 Stokes Theorem 1209 2
Page 2435:
Section 16.7 Stokes Theorem 1211 C
Page 2439:
Section 16.8 The Divergence Theorem
Page 2443:
Page 2447:
Page 2451:
30. By Exercise 29, 2 f g d f g f g
Page 2455:
Page 2459:
Page 2463:
Page 2467:
Page 2471:
Page 2475:
Page 2479:
Page 2483:
CHAPTER 17 SECOND-ORDER DIFFERENTIA
Page 2487:
ww w w 2 2 Section 17.1 Second-Orde
Page 2491:
Section 17.1 Second-Order Linear Eq
Page 2495:
Section 17.2 Nonhomogeneous Linear
Page 2499:
Section 17.2 Nonhomogeneous Linear
Page 2503:
2 dy dx dy dx Section 17.2 Nonhomog
Page 2507:
dy w dx œc1sin x c2cos x cos xlnks
Page 2511:
Section 17.3 Applications 1017 ! !
Page 2515:
5 10 5È 2 2 5 dy 5È2 dy 1 16 $ È
Page 2519:
Section 17.4 Euler Equations 1021 "
Page 2523:
Section 17.5 Power-Series Soutions
Page 2527:
∞ ∞ ∞ # ww w # 5. x y 2xy 2
Page 2531:
# ww # 11. x 1y 6y 0 x 1 n2 nn 1c x
Page 2535:
∞ ∞ ∞ ww w 17. y xy 3y œ 0
show all

Thomas Calculus 13th [Solutions]

Create successful ePaper yourself

Delete template?

Save as template?