James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

A100 Appendix I Answers to Odd-Numbered Exercises
27. n T n M n S n
6 6.695473 6.252572 6.403292
12 6.474023 6.363008 6.400206
n E T E M E S
6 20.295473 0.147428 20.003292
12 20.074023 0.036992 20.000206
Observations are the same as after Example 1.
29. (a) 19 (b) 18.6 (c) 18.6
31. (a) 14.4 (b) 1 2
33. 70.8°F 35. 37.73 ftys 37. 10,177 megawatt-hours
39. (a) 190 (b) 828
41. 28 43. 59.4
45. y
1
0 0.5 1 1.5 2 x
Exercises 5et070743 7.8 • page 534
Solution Ar t
Abbreviations: C, convergent; D, divergent
6.26.02
1. (a), (d) Infinite discontinuity (b), (c) Infinite interval
3. 1 2 2 1ys2t 2 d; 0.495, 0.49995, 0.4999995; 0.5
5. 2 7. D 9. 1 5 e210 11. D 13. 0 15. D
17. ln 2 19. 2 1 4 21. D 23. 2y8 25. 2
27. D 29. 32 3 31. D 33. 9 2 35. D 37. 21 4
39. 22ye
41. 1ye 43. 1 2 ln 2
2
y
y=e _x 1
y=
˛+x
x=1
0 1
45. Infinite area
20
0
47. (a)
ca051037
10.31.00
y=sec@ x
t
x
π
2
0
y t
fssin 2 xdyx 2 g dx
1
2 0.447453
5 0.577101
10 0.621306
100 0.668479
1,000 0.672957
10,000 0.673407
It appears that the integral is convergent.
3
(c) 1
1 10
0.1
ƒ= 1 ≈
©= sin@ x
≈
49. C 51. D 53. D 55. 57. p , 1, 1ys1 2 pd
59. p . 21, 21ysp 1 1d 2 63. 65. s2GMyR
67. (a) y
1
(b) The rate at which the
y=F(t)
fraction Fstd increases as t
increases
(c) 1; all bulbs burn out
eventually
0
700 t
(in hours)
cN
69. −
71. 1000
sk 1 d
73. (a) Fssd − 1ys, s . 0 (b) Fssd − 1yss 2 1d, s . 1
(c) Fssd − 1ys 2 , s . 0
79. C − 1; ln 2 81. No
Chapter 7 Review • page 537
True-False Quiz
1. False 3. False 5. False 7. False
9. (a) True (b) False 11. False 13. False
Exercises
1. 7 2 1 ln 2 3. e sin x 1 C 5. ln| 2t 1 1 | 2 ln | t 1 1 | 1 C
7.
2
15 9. 2cossln td 1 C 11. s3 2 1 3
13. 3e s3 x
sx 2y3 2 2x 1y3 1 2d 1 C
15. 2 1 2 ln | x | 1 3 2 ln | x 1 2 | 1 C
17. x sinh x 2 cosh x 1 C
19.
1
18 lns9x 2 1 6x 1 5d 1 1 9 f tan21 1 2 s3x 1 1dg 1 C
21. ln | x 2 2 1 sx 2 2 4x | 1 C
Z 1 C
sx
23. ln Z 2 1 1 2 1
x
25. 3 2 lnsx 2 1 1d 2 3 tan 21 x 1 s2 tan 21 (xys2 ) 1 C
27. 2 5 29. 0 31. 21S 6 2 3 2
x
33. 2 sin x 1 C
s4 2 x 2D 2
35. 4s1 1 sx 1 C 37. 1 2 sin 2x 2 1 8 cos 4x 1 C
39. 1 8 e 2 1 4 41. 1 36 43. D
45. 4 ln 4 2 8 47. 2 4 3
49. y4
51. sx 1 1d lnsx 2 1 2x 1 2d 1 2 arctansx 1 1d 2 2x 1 C
53. 0
55. 1 4 s2x 2 1ds4x2 2 4x 2 3
2 ln | 2x 2 1 1 s4x 2 2 4x 2 3 | 1 C
57. 1 2 sin xs4 1 sin2 x 1 2 lnssin x 1 s4 1 sin 2 x d 1 C
61. No
63. (a) 1.925444 (b) 1.920915 (c) 1.922470
65. (a) 0.01348, n > 368 (b) 0.00674, n > 260
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