Thomas Calculus 13th [Solutions]

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75. (a) Perihelion a ae a(1 e ), Aphelion ea a a(1 e) (b) Planet Perihelion Aphelion Mercury 0.3075 AU 0.4667 AU Venus 0.7184 AU 0.7282 AU Earth 0.9833 AU 1.0167 AU Mars 1.3817 AU 1.6663 AU Jupiter 4.9512 AU 5.4548 AU Saturn 9.0210 AU 10.0570 AU Uranus 18.2977 AU 20.0623 AU Neptune 29.8135 AU 30.3065 AU Section 11.7 Conics in Polar Coordinates 859 76. 2 (0.3871) 1 0.2056 Mercury: r 0.3707 1 0.2056 cos 1 0.2056 cos 2 (0.7233) 1 0.0068 Venus: r 0.7233 1 0.0068 cos 1 0.0068 cos 2 1 1 0.0167 Earth: r 0.9997 1 0.0167 cos 1 0.0617 cos 2 (1.524) 1 0.0934 Mars: r 1.511 1 0.0934 cos 1 0.0934 cos 2 (5.203) 1 0.0484 Jupiter: r 5.191 1 0.0484 cos 1 0.0484 cos 2 (9.539) 1 0.0543 Saturn: r 9.511 1 0.0543 cos 1 0.0543 cos 2 (19.18) 1 0.0460 Uranus : r 19.14 1 0.0460cos 1 0.0460cos 2 (30.06) 1 0.0082 Neptune: r 30.06 1 0.0082 cos 1 0.0082 cos Copyright 2014 Pearson Education, Inc.
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1 Functions 1 TABLE OF CONTENTS 1.1
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8.3 Trigonometric Integrals 569 8.4
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2 Chapter 1 Functions 15. The domai
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4 Chapter 1 Functions 3 0 0 ( 1) 1
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6 Chapter 1 Functions 43. Symmetric
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8 Chapter 1 Functions 68. (a) From
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10 Chapter 1 Functions The complete
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12 Chapter 1 Functions 35. 36. 37.
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14 Chapter 1 Functions (c) domain:
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16 Chapter 1 Functions 69. 3 y f (
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18 Chapter 1 Functions (c) (d) 80.
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20 Chapter 1 Functions 21. 22. peri
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22 Chapter 1 Functions 40. sin(2 x)
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24 Chapter 1 Functions 65. A 2, B 2
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26 Chapter 1 Functions 1.4 GRAPHING
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28 Chapter 1 Functions 17. [ 5, 1]
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30 Chapter 1 Functions 35. 36. 37.
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32 Chapter 1 Functions 9. 10. 11. 2
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34 Chapter 1 Functions 35. After t
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36 Chapter 1 Functions 24. Step 1:
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38 Chapter 1 Functions y 1 36. y =
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40 Chapter 1 Functions 56. (a) (b)
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42 Chapter 1 Functions 1 50 50 50 (
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44 Chapter 1 Functions 10. 5 3 5 y(
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46 Chapter 1 Functions 37. (a) ( f
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48 Chapter 1 Functions 50. (a) Shif
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50 Chapter 1 Functions 65. Let h he
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52 Chapter 1 Functions 81. (a) No (
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54 Chapter 1 Functions 11. If f is
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56 Chapter 1 Functions 21. (a) y =
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58 Chapter 1 Functions Copyright 20
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60 Chapter 2 Limits and Continuity
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116 Chapter 3 Derivatives 9. m 3 3
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118 Chapter 3 Derivatives 32. (2 )
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120 Chapter 3 Derivatives 45. (a) T
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122 Chapter 3 Derivatives 2. 2 2 F(
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124 Chapter 3 Derivatives 18. 19. (
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126 Chapter 3 Derivatives (b) The t
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128 Chapter 3 Derivatives 48. (a) f
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130 Chapter 3 Derivatives 59. The g
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132 Chapter 3 Derivatives 6. y 3 2
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134 Chapter 3 Derivatives 33. 34. 3
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136 Chapter 3 Derivatives 56. (a) 3
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138 Chapter 3 Derivatives 74. (a) W
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140 Chapter 3 Derivatives 10 . (a)
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142 Chapter 3 Derivatives 25. 6 4 3
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144 Chapter 3 Derivatives 36. (a) v
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146 Chapter 3 Derivatives 25. r sec
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148 Chapter 3 Derivatives 44. We wa
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150 Chapter 3 Derivatives 64. cos(
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152 Chapter 3 Derivatives 3.6 THE C
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154 Chapter 3 Derivatives y 1 6 1 1
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156 Chapter 3 Derivatives 58. sin(
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158 Chapter 3 Derivatives 82. g( x)
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160 Chapter 3 Derivatives (b) y sin
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162 Chapter 3 Derivatives (c) df dt
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168 Chapter 3 Derivatives 47. 2 2 x
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170 Chapter 3 Derivatives Mathemati
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172 Chapter 3 Derivatives 13. y 2 l
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174 Chapter 3 Derivatives 44. 1 1/2
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178 Chapter 3 Derivatives 100. Supp
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180 Chapter 3 Derivatives 3.9 INVER
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184 Chapter 3 Derivatives 60. (a) D
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186 Chapter 3 Derivatives 65. The v
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188 Chapter 3 Derivatives 2 2 2 2 2
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190 Chapter 3 Derivatives 35. 1 dy
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192 Chapter 3 Derivatives 3.11 LINE
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194 Chapter 3 Derivatives x x x x 3
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196 Chapter 3 Derivatives 2 dA dt d
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198 Chapter 3 Derivatives As one zo
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200 Chapter 3 Derivatives 12. y 1 2
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202 Chapter 3 Derivatives 43. 1 4x
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204 Chapter 3 Derivatives 72. 2 1/2
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206 Chapter 3 Derivatives 90. 2 t 2
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208 Chapter 3 Derivatives 104. y si
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210 Chapter 3 Derivatives 124. rabb
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212 Chapter 3 Derivatives 147. Give
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214 Chapter 3 Derivatives CHAPTER 3
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216 Chapter 3 Derivatives 2 (b) On
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218 Chapter 3 Derivatives k k k k d
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220 Chapter 4 Applications of Deriv
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344 Chapter 5 Integration 3. f ( x
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346 Chapter 5 Integration 13. (a) B
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348 Chapter 5 Integration for n in
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350 Chapter 5 Integration n n 17. (
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352 Chapter 5 Integration 34. (a) (
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354 Chapter 5 Integration 45. 3 f (
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356 Chapter 5 Integration 2 2 17. T
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358 Chapter 5 Integration 33. 3 3 3
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360 Chapter 5 Integration b b 54. L
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362 Chapter 5 Integration 62. (a) 1
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364 Chapter 5 Integration 3 1 2 1 n
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366 Chapter 5 Integration (c) av( f
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368 Chapter 5 Integration 95-102. E
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370 Chapter 5 Integration 10. (1 co
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372 Chapter 5 Integration 34. 0 x 1
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374 Chapter 5 Integration 57. 2 x 2
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376 Chapter 5 Integration 71. Area
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378 Chapter 5 Integration 85 88. Ex
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380 Chapter 5 Integration 2 1 2 2 4
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382 Chapter 5 Integration 3 2 2 27.
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384 Chapter 5 Integration x 53. Let
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386 Chapter 5 Integration 72. csc x
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388 Chapter 5 Integration (b) Use t
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390 Chapter 5 Integration 17. Let u
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394 Chapter 5 Integration 2 3 54. F
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396 Chapter 5 Integration 65. a 0,
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398 Chapter 5 Integration 73. Limit
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400 Chapter 5 Integration 2 4 81. L
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402 Chapter 5 Integration 91. c 0,
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404 Chapter 5 Integration (c) 2 c f
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406 Chapter 5 Integration 116. Let
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408 Chapter 5 Integration 3. (a) (b
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410 Chapter 5 Integration 15. f ( x
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412 Chapter 5 Integration 27. f ( y
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416 Chapter 5 Integration 68. dx du
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418 Chapter 5 Integration 90. 3 /4
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420 Chapter 5 Integration 110. 8 8
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422 Chapter 5 Integration 130. The
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424 Chapter 5 Integration 8. The de
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426 Chapter 5 Integration 3 24. Let
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428 Chapter 5 Integration 36. y 3 x
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430 Chapter 5 Integration Copyright
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432 Chapter 6 Applications of Defin
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508 Chapter 7 Integrals and Transce
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536 Chapter 7 Transcendental Functi
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544 Chapter 8 Techniques of Integra
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662 Chapter 9 First-Order Different
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702 Chapter 10 Infinite Sequences a
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802 Chapter 11 Parametric Equations
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Page 1755: CHAPTER 11 ADDITIONAL AND ADVANCED
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Page 1767: CHAPTER 12 VECTORS AND THE GEOMETRY
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Section 12.2 Vectors 885 F 1 sin 40
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Section 12.3 The Dot Product 887 11
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Section 12.4 The Cross Product 893
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23. (a) u v 6, u w 81, v w 18 none
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Section 12.4 The Cross Product 897
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Section 12.5 Lines and Planes in Sp
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L1 & L3: x 3 2t 3 2r 2t 2r 0 t r 0
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Section 12.6 Cylinders and Quadric
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Chapter 12 Practice Exercises 913 1
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i j k Chapter 12 Practice Exercises
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Chapter 12 Practice Exercises 919 (
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Chapter 12 Additional and Advanced
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CHAPTER 13 VECTOR-VALUED FUNCTIONS
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Section 13.1 Curves in Space and Th
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Section 13.1 Curves in Space and Th
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Section 13.2 Integrals of Vector Fu
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dr dt Section 13.2 Integrals of Vec
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t Section 13.3 Arc Length in Space
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Section 13.3 Arc Length in Space 94
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Section 13.4 Curvature and Normal V
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8. (a) Section 13.4 Curvature and N
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Section 13.5 Tangential and Normal
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Section 13.6 Velocity and Accelerat
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13. Assuming Earth has a circular o
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Chapter 13 Practice Exercises 963 i
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i j k 9. (a) ur u cos sin 0 k a rig
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CHAPTER 14 PARTIAL DERIVATIVES 14.1
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17. (a) Domain: all points in the x
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Section 14.1 Functions of Several V
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44. (a) (b) Section 14.1 Functions
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Section 14.2 Limits and Continuity
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Section 14.3 Partial Derivatives 99
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Section 14.4 The Chain Rule 999 92.
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Section 14.4 The Chain Rule 1001 w
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Section 14.4 The Chain Rule 1003 18
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Section 14.4 The Chain Rule 1005 y
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Section 14.4 The Chain Rule 1007 46
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Section 14.5 Directional Derivative
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Section 14.6 Tangent Planes and Dif
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Section 14.7 Extreme Values and Sad
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2 33. (i) On OA, f ( x, y) f (0, y)
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38. (i) On OA, f ( x, y) f (0, y) 2
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5. We optimize Section 14.8 Lagrang
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15. T (8x 4 y) i ( 4x 2 y) j and Se
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Section 14.8 Lagrange Multipliers 1
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34. Q( p, q, r) 2( pq pr qr ) and G
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Section 14.8 Lagrange Multipliers 1
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49-54. Example CAS commands: Maple:
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Section 14.9 Taylors Formula for Tw
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Section 14.10 Partial Derivatives w
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Section 14.10 Partial Derivatives w
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Chapter 14 Practice Exercises 1059
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74. (i) On OA, 2 f ( x, y) f (0, y)
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(iii) On CD, 3 f ( x, y) f (1, y) y
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96. Let Chapter 14 Practice Exercis
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21. (a) k is a vector normal to wil
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CHAPTER 15 MULTIPLE INTEGRALS 15.1
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Section 15.1 Double and Iterated In
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7. 8. Section 15.2 Double Integrals
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Section 15.2 Double Integrals Over
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Section 15.3 Area by Double Integra
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Section 15.3 Area by Double Integra
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Section 15.4 Double Integrals in Po
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6. The projection of D onto the xy
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Section 15.5 Triple Integrals in Re
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Section 15.5 Triple Integrals in Re
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Section 15.6 Moments and Centers of
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Section 15.7 Triple Integrals in Cy
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66. average 1 2 3 Section 15.7 Trip
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Section 15.8 Substitutions in Multi
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53. x u y and y v x u v and y v 1 1
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CHAPTER 16 INTEGRALS AND VECTOR FIE
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Section 16.1 Line Integrals 1157 1
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Section 16.1 Line Integrals 1159 34
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Section 16.2 Vector Fields and Line
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(b) Section 16.2 Vector Fields and
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11. 2 2 Section 16.3 Path Independe
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Section 16.3 Path Independence, Pot
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Section 16.3 Path Independence, Pot
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Section 16.4 Greens Theorem in the
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Section 16.5 Surfaces and Area 1185
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(b) In a fashion similar to cylindr
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Section 16.6 Surface Integrals 1197
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Section 16.7 Stokes Theorem 1207 i
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Section 16.7 Stokes Theorem 1209 2
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Section 16.7 Stokes Theorem 1211 C
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Section 16.8 The Divergence Theorem
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30. By Exercise 29, 2 f g d f g f g
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CHAPTER 17 SECOND-ORDER DIFFERENTIA
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ww w w 2 2 Section 17.1 Second-Orde
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Section 17.1 Second-Order Linear Eq
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Section 17.2 Nonhomogeneous Linear
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Section 17.2 Nonhomogeneous Linear
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2 dy dx dy dx Section 17.2 Nonhomog
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dy w dx œc1sin x c2cos x cos xlnks
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Section 17.3 Applications 1017 ! !
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5 10 5È 2 2 5 dy 5È2 dy 1 16 $ È
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Section 17.4 Euler Equations 1021 "
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Section 17.5 Power-Series Soutions
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∞ ∞ ∞ # ww w # 5. x y 2xy 2
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# ww # 11. x 1y 6y 0 x 1 n2 nn 1c x
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∞ ∞ ∞ ww w 17. y xy 3y œ 0
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Thomas Calculus 13th [Solutions]

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