Thomas Calculus 13th [Solutions]

Recommendations

Info

48 Chapter 1 Functions 50. (a) Shift the graph of f right 5 units (b) Horizontally compress the graph of f by a factor of 4 (c) Horizontally compress the graph of f by a factor of 3 and then reflect the graph about the y-axis (d) Horizontally compress the graph of f by a factor of 2 and then shift the graph left 1 2 unit. (e) Horizontally stretch the graph of f by a factor of 3 and then shift the graph down 4 units. (f ) Vertically stretch the graph of f by a factor of 3, then reflect the graph about the x-axis, and finally shift the graph up 1 4 unit. 51. Reflection of the graph of y x about the x-axis followed by a horizontal compression by a factor of 1 then a shift left 2 units. 2 52. Reflect the graph of y x about the x-axis, followed by a vertical compression of the graph by a factor of 3, then shift the graph up 1 unit. 53. Vertical compression of the graph of y 1 by a 2 x factor of 2, then shift the graph up 1 unit. 1/3 54. Reflect the graph of y x about the y-axis, then compress the graph horizontally by a factor of 5. 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 111: Chapter 1 Practice Exercises 49 55.
Page 115: 70. (a) D ( , 0) (0, ) (b) D ( , 2)
Page 119: Chapter 1 Additional and Advanced E
Page 131: CHAPTER 2 LIMITS AND CONTINUITY 2.1
Page 135: 19. (a) (b) g( x) g g(2) g(1) 2 1 x
Page 139: Section 2.2 Limit of a Function and
Page 159:
Section 2.3 The Precise Definition
Page 163:
Page 167:
Page 171:
Page 175:
Section 2.4 One-Sided Limits 81 2.4
Page 179:
Section 2.4 One-Sided Limits 83 17.
Page 183:
Section 2.4 One-Sided Limits 85 44.
Page 187:
Section 2.5 Continuity 87 19. Disco
Page 191:
Section 2.5 Continuity 89 49. The f
Page 195:
Section 2.5 Continuity 91 65. Yes,
Page 199:
13. (a) 2 3 2 lim x x lim 2 x x 5 7
Page 203:
Section 2.6 Limits Involving Infini
Page 207:
Page 211:
Page 215:
Page 219:
Chapter 2 Practice Exercises 103 2.
Page 223:
Chapter 2 Practice Exercises 105 17
Page 227:
Page 231:
Chapter 2 Additional and Advanced E
Page 235:
Page 239:
Page 243:
CHAPTER 3 DERIVATIVES 3.1 TANGENTS
Page 247:
Section 3.1 Tangents and the Deriva
Page 251:
Section 3.1 Tangents and the Deriva
Page 255:
Section 3.2 The Derivative as a Fun
Page 259:
Page 263:
Page 267:
Right-hand derivative: When h 0,1 h
Page 271:
Page 275:
63-68. Example CAS commands: Maple:
Page 279:
Section 3.3 Differentiation Rules 1
Page 283:
Page 287:
Page 291:
Section 3.4 The Derivative as a Rat
Page 295:
Page 299:
Page 303:
Section 3.5 Derivatives of Trigonom
Page 307:
Page 311:
Page 315:
Page 319:
Section 3.6 The Chain Rule 153 2 2
Page 323:
Section 3.6 The Chain Rule 155 44.
Page 327:
Page 331:
Section 3.6 The Chain Rule 159 11 2
Page 335:
Section 3.6 The Chain Rule 161 sin
Page 339:
Section 3.7 Implicit Differentiatio
Page 343:
Page 347:
Page 351:
Page 355:
Section 3.8 Derivatives of Inverse
Page 359:
Page 363:
Page 367:
Page 371:
109 110. Example CAS commands: Sect
Page 375:
Section 3.9 Inverse Trigonometric F
Page 379:
Page 383:
Page 387:
Section 3.10 Related Rates 187 5. y
Page 391:
Section 3.10 Related Rates 189 27.
Page 395:
Section 3.10 Related Rates 191 43.
Page 399:
Section 3.11 Linearization and Diff
Page 403:
Page 407:
Page 411:
plot(err(x), x 1..2, title #absolut
Page 415:
Page 419:
Page 423:
Page 427:
Chapter 3 Practice Exercises 207 (b
Page 431:
Page 435:
Page 439:
Chapter 3 Practice Exercises 213 (b
Page 443:
Page 447:
Page 451:
CHAPTER 4 APPLICATIONS OF DERIVATIV
Page 455:
Section 4.1 Extreme Values of Funct
Page 459:
Page 463:
Page 467:
Page 471:
Page 475:
Page 479:
Section 4.2 The Mean Value Theorem
Page 483:
27. r ( ) sec 1 5 ( ) (sec )(tan )
Page 487:
Section 4.2 The Mean Value Theorem
Page 491:
Section 4.3 Monotonic Functions and
Page 495:
Page 499:
33. (a) 34. (a) 35. (a) 2 2 1/2 g(
Page 503:
Page 507:
Page 511:
(b) The graph of f rises when f 0,
Page 515:
Page 519:
86. f(x) is increasing since 1 5/3
Page 523:
Section 4.4 Concavity and Curve Ske
Page 527:
5 4 21. When y x 5 x , then 4 3 3 3
Page 531:
31. When y x , then y 1 and x 2 2 3
Page 535:
2 2 40. When y x , then x y 2 x 2 2
Page 539:
Page 543:
Page 547:
Page 551:
Page 555:
Page 559:
Page 563:
The line x 2 is a vertical asymptot
Page 567:
104. 105. Section 4.4 Concavity and
Page 571:
3 2 2 Section 4.4 Concavity and Cur
Page 575:
Section 4.5 Indeterminate Forms and
Page 579:
Page 583:
Page 587:
Page 591:
Page 595:
Section 4.6 Applied Optimization 29
Page 599:
16. (a) The base measures 10 2x in.
Page 603:
2 3 Section 4.6 Applied Optimizatio
Page 607:
Page 611:
Page 615:
Page 619:
Page 623:
Section 4.7 Newtons Method 305 4. 2
Page 627:
Section 4.7 Newtons Method 307 20.
Page 631:
Section 4.8 Antiderivatives 309 4.8
Page 635:
Section 4.8 Antiderivatives 311 42.
Page 639:
85. (a) Wrong: (b) (c) d dx 3 (2x 1
Page 643:
Section 4.8 Antiderivatives 315 2 2
Page 647:
Section 4.8 Antiderivatives 317 128
Page 651:
Page 655:
Page 659:
45. (a) y 6 x( x 1)( x 2) (b) 3 2 6
Page 663:
52. The graph of the first derivati
Page 667:
Page 671:
92. (a) The distance between the pa
Page 675:
Page 679:
Page 683:
Chapter 4 Practice Exercises 335 x
Page 687:
Page 691:
Page 695:
Page 699:
CHAPTER 5 INTEGRATION 5.1 AREA AND
Page 703:
Section 5.1 Area and Estimating wit
Page 707:
Section 5.1 Area and Estimating wit
Page 711:
Section 5.2 Sigma Notation and Limi
Page 715:
Page 719:
Page 723:
Section 5.3 The Definite Integral 3
Page 727:
Page 731:
Page 735:
Page 739:
65. Consider the partition P that s
Page 743:
74. See Exercise 73 above. On [0, 0
Page 747:
Page 751:
Section 5.4 The Fundamental Theorem
Page 755:
Page 759:
Page 763:
Page 767:
Page 771:
93. Example CAS commands: Maple: f
Page 775:
Section 5.5 Indefinite Integrals an
Page 779:
Page 783:
Page 787:
80. Let 2 u t du dt du dt Section 5
Page 791:
1 1 11. (a) Let u 4 5 t t ( u 4), d
Page 795:
Section 5.6 Substitution and Area B
Page 799:
Page 803:
61. AREA A1 A2 A3 A1: For the sketc
Page 807:
Page 811:
Page 815:
Page 819:
Page 823:
Page 827:
Chapter 5 Practice Exercises 407 CH
Page 831:
Page 835:
Page 839:
Page 843:
Page 847:
80. Let u 7 5r du 5 dr 1 du dr; r 0
Page 851:
Page 855:
Page 859:
Page 863:
Page 867:
29. (a) (b) 1 g(1) f ( t) dt 0 1 3
Page 871:
Page 875:
CHAPTER 6 APPLICATIONS OF DEFINITE
Page 879:
Section 6.1 Volumes Using Cross-Sec
Page 883:
Page 887:
Page 891:
Page 895:
Page 899:
Section 6.2 Volumes Using Cylindric
Page 903:
Page 907:
Page 911:
Page 915:
Page 919:
Page 923:
Section 6.3 Arc Length 455 2. dy 3
Page 927:
Section 6.3 Arc Length 457 9. dx 1
Page 931:
Section 6.3 Arc Length 459 19. (a)
Page 935:
Section 6.3 Arc Length 461 32. (a)
Page 939:
Section 6.4 Areas of Surfaces of Re
Page 943:
Page 947:
Page 951:
Section 6.5 Work and Fluid Forces 4
Page 955:
(d) In a location where water weigh
Page 959:
Page 963:
Page 967:
38. Using the coordinate system giv
Page 971:
Section 6.6 Moments and Centers of
Page 975:
mass: 2 dm dA 3 1 x dx . The moment
Page 979:
Page 983:
Page 987:
Page 991:
Page 995:
Page 999:
Chapter 6 Practice Exercises 493 6.
Page 1003:
(b) shell method: Chapter 6 Practic
Page 1007:
Chapter 6 Practice Exercises 497 x
Page 1011:
Page 1015:
(a) Chapter 6 Additional and Advanc
Page 1019:
10. Converting to pounds and feet,
Page 1023:
Page 1027:
CHAPTER 7 INTEGRALS AND TRANSCENDEN
Page 1031:
Section 7.1 The Logarithm Defined a
Page 1035:
Section 7.1 The Logarithm Defined a
Page 1039:
61. y = ln kx y = ln x + ln k; thus
Page 1043:
Section 7.2 Exponential Change and
Page 1047:
Section 7.2 Exponential Change and
Page 1051:
37. 0 kt A A e and Section 7.2 Expo
Page 1055:
Section 7.3 Hyperbolic Functions 52
Page 1059:
Page 1063:
Page 1067:
Page 1071:
Section 7.4 Relative Rates of Growt
Page 1075:
Page 1079:
Page 1083:
Chapter 7 Practice Exercises 535 CH
Page 1087:
Chapter 7 Practice Exercises 537 (d
Page 1091:
Page 1095:
Page 1099:
CHAPTER 8 TECHNIQUES OF INTEGRATION
Page 1103:
Section 8.1 Using Basic Integration
Page 1107:
Page 1111:
Page 1115:
Page 1119:
Page 1123:
Section 8.2 Integration by Parts 55
Page 1127:
Page 1131:
Page 1135:
Page 1139:
Page 1143:
Page 1147:
Page 1151:
Section 8.3 Trigonometric Integrals
Page 1155:
Page 1159:
Page 1163:
Page 1167:
Section 8.4 Trigonometric Substitut
Page 1171:
Page 1175:
Page 1179:
Page 1183:
Section 8.5 Integration of Rational
Page 1187:
Page 1191:
Page 1195:
Page 1199:
Page 1203:
Section 8.6 Integral Tables and Com
Page 1207:
Page 1211:
Page 1215:
Page 1219:
Page 1223:
Page 1227:
Section 8.7 Numerical Integration 6
Page 1231:
Page 1235:
Page 1239:
Page 1243:
Page 1247:
Section 8.8 Improper Integrals 617
Page 1251:
Page 1255:
Page 1259:
1 sin x 56. 2 x 1 sin x dx; 0 2 2 2
Page 1263:
Page 1267:
Page 1271:
Section 8.9 Probability 629 In orde
Page 1275:
Section 8.9 Probability 631 20. 3/2
Page 1279:
Section 8.9 Probability 633 36. For
Page 1283:
Section 8.9 Probability 635 52 . 20
Page 1287:
Page 1291:
Chapter 8 Practice Exercises 639 (3
Page 1295:
Page 1299:
Chapter 8 Practice Exercises 643 d
Page 1303:
Page 1307:
Chapter 8 Practice Exercises 647 3/
Page 1311:
Chapter 8 Practice Exercises 649 li
Page 1315:
Page 1319:
Page 1323:
Page 1327:
Page 1331:
t b t t Chapter 8 Additional and Ad
Page 1335:
CHAPTER 9 FIRST-ORDER DIFFERENTIAL
Page 1339:
Section 9.1 Solutions, Slope Fields
Page 1343:
Page 1347:
Page 1351:
Page 1355:
Section 9.2 First-Order Linear Equa
Page 1359:
Section 9.2 First-Order Linear Equa
Page 1363:
Section 9.3 Applications 675 6. 2 2
Page 1367:
14. (a) dV (5 3) 2 V 100 2t dt The
Page 1371:
Section 9.4 Graphical Solutions of
Page 1375:
Page 1379:
Page 1383:
Section 9.4 Graphical Solution of A
Page 1387:
Implies coexistence is not possible
Page 1391:
Section 9.5 Systems of Equations an
Page 1395:
Section 9.5 Systems of Equations an
Page 1399:
Page 1403:
Page 1407:
Page 1411:
Page 1415:
CHAPTER 10 INFINITE SEQUENCES AND S
Page 1419:
Section 10.1 Sequences 703 40. 1 n
Page 1423:
Section 10.1 Sequences 705 70. 1 n
Page 1427:
95. Since a n converges Section 10.
Page 1431:
111. 3( n 1) 1 3 1 3 4 3 1 2 2 a n
Page 1435:
Section 10.1 Sequences 711 133. a2k
Page 1439:
Section 10.2 Infinite Series 713 12
Page 1443:
Page 1447:
Page 1451:
Page 1455:
6. f ( x ) 1 is positive, continuou
Page 1459:
Section 10.3 The Integral Test 723
Page 1463:
Page 1467:
Page 1471:
Section 10.4 Comparison Tests 729 4
Page 1475:
Page 1479:
Page 1483:
Page 1487:
Page 1491:
Section 10.5 Absolute Convergence;
Page 1495:
Page 1499:
Page 1503:
Section 10.6 Alternating Series and
Page 1507:
Page 1511:
Page 1515:
Page 1519:
Section 10.7 Power Series 753 6. n
Page 1523:
Section 10.7 Power Series 755 17. l
Page 1527:
Section 10.7 Power Series 757 25. n
Page 1531:
Section 10.7 Power Series 759 1 2 1
Page 1535:
Section 10.7 Power Series 761 inter
Page 1539:
Section 10.7 Power Series 763 3 5 1
Page 1543:
Section 10.8 Taylor and Maclaurin S
Page 1547:
Section 10.8 Taylor and Maclaurin S
Page 1551:
Section 10.9 Convergence of Taylor
Page 1555:
Page 1559:
Page 1563:
Page 1567:
Section 10.10 The Binomial Series a
Page 1571:
Page 1575:
Page 1579:
Page 1583:
Page 1587:
Page 1591:
Page 1595:
Page 1599:
Page 1603:
Chapter 10 Additional and Advanced
Page 1607:
Page 1611:
Page 1615:
CHAPTER 11 PARAMETRIC EQUATIONS AND
Page 1619:
Section 11.1 Parametrizations of Pl
Page 1623:
Page 1627:
Page 1631:
Section 11.2 Calculus with Parametr
Page 1635:
Page 1639:
Page 1643:
Page 1647:
Page 1651:
Section 11.3 Polar Coordinates 819
Page 1655:
Page 1659:
Page 1663:
Section 11.4 Graphing Polar Coordin
Page 1667:
Page 1671:
Page 1675:
Page 1679:
9. r 2cos and r 2sin 2cos 2sin cos
Page 1683:
17. r sec and A r 2 4cos 4cos sec c
Page 1687:
Section 11.5 Areas and Lengths in P
Page 1691:
Section 11.6 Conic Sections 839 9.
Page 1695:
Page 1699:
Page 1703:
Page 1707:
Page 1711:
Section 11.7 Conics in Polar Coordi
Page 1715:
Page 1719:
Page 1723:
Page 1727:
Page 1731:
75. (a) Perihelion a ae a(1 e ), Ap
Page 1735:
Page 1739:
Page 1743:
Page 1747:
Page 1751:
Page 1755:
CHAPTER 11 ADDITIONAL AND ADVANCED
Page 1759:
Page 1763:
Page 1767:
CHAPTER 12 VECTORS AND THE GEOMETRY
Page 1771:
Section 12.1 Three-Dimensional Coor
Page 1775:
Section 12.2 Vectors 881 66. 2 2 2
Page 1779:
Section 12.2 Vectors 883 25. length
Page 1783:
Section 12.2 Vectors 885 F 1 sin 40
Page 1787:
Section 12.3 The Dot Product 887 11
Page 1791:
Page 1795:
Page 1799:
Section 12.4 The Cross Product 893
Page 1803:
23. (a) u v 6, u w 81, v w 18 none
Page 1807:
Section 12.4 The Cross Product 897
Page 1811:
Section 12.5 Lines and Planes in Sp
Page 1815:
Page 1819:
Page 1823:
L1 & L3: x 3 2t 3 2r 2t 2r 0 t r 0
Page 1827:
Section 12.6 Cylinders and Quadric
Page 1831:
Page 1835:
Page 1839:
Page 1843:
Page 1847:
i j k Chapter 12 Practice Exercises
Page 1851:
Chapter 12 Practice Exercises 919 (
Page 1855:
Page 1859:
Page 1863:
Page 1867:
CHAPTER 13 VECTOR-VALUED FUNCTIONS
Page 1871:
Section 13.1 Curves in Space and Th
Page 1875:
Section 13.1 Curves in Space and Th
Page 1879:
Section 13.2 Integrals of Vector Fu
Page 1883:
Page 1887:
dr dt Section 13.2 Integrals of Vec
Page 1891:
Page 1895:
t Section 13.3 Arc Length in Space
Page 1899:
Section 13.3 Arc Length in Space 94
Page 1903:
Section 13.4 Curvature and Normal V
Page 1907:
8. (a) Section 13.4 Curvature and N
Page 1911:
Page 1915:
Page 1919:
Section 13.5 Tangential and Normal
Page 1923:
Page 1927:
Page 1931:
Section 13.6 Velocity and Accelerat
Page 1935:
13. Assuming Earth has a circular o
Page 1939:
Chapter 13 Practice Exercises 963 i
Page 1943:
Page 1947:
Page 1951:
Page 1955:
i j k 9. (a) ur u cos sin 0 k a rig
Page 1959:
CHAPTER 14 PARTIAL DERIVATIVES 14.1
Page 1963:
17. (a) Domain: all points in the x
Page 1967:
Section 14.1 Functions of Several V
Page 1971:
44. (a) (b) Section 14.1 Functions
Page 1975:
Page 1979:
Page 1983:
Section 14.2 Limits and Continuity
Page 1987:
Page 1991:
Page 1995:
Section 14.3 Partial Derivatives 99
Page 1999:
Page 2003:
Page 2007:
Page 2011:
Page 2015:
Section 14.4 The Chain Rule 1001 w
Page 2019:
Section 14.4 The Chain Rule 1003 18
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 2035:
Page 2039:
Page 2043:
Section 14.6 Tangent Planes and Dif
Page 2047:
Page 2051:
Page 2055:
Page 2059:
Page 2063:
Section 14.7 Extreme Values and Sad
Page 2067:
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:
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:
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:
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]

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

Delete template?

Save as template?