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

Appendix I Answers to Odd-Numbered Exercises A97
Exercises 6.5 • page 463
1. 7 3. 6y 5. s2ydse 2 1d 7. 2ys5d
9. (a) 1 (b) 2, 4 (c)
11. (a) 4y (b) <1.24, 2.81
(c)
Chapter 7
Exercises 7.1 • page 476
1. 1 2 xe 2x 2 1 4 e 2x 1 C 3. 1 5 x sin 5x 1 1 25 cos 5x 1 C
5. 2 1 3 te23t 2 1 9 e23t 1 C
7. sx 2 1 2xd sin x 1 s2x 1 2d cos x 2 2 sin x 1 C
9. x cos 21 x 2 s1 2 x 2 1 C 11. 1 5 t 5 ln t 2 1 25 t 5 1 C
13. 2t cot t 1 ln | sin t | 1 C
15. xsln xd 2 2 2x ln x 1 2x 1 C
1
17. 13 e 2 s2 sin 3 2 3 cos 3d 1 C
19. z 3 e z 2 3z 2 e z 1 6ze z 2 6e z 1 C
e 2x
21.
4s2x 1 1d 1 C 23. 2 2
2 2
25. 2 cosh 2 2 sinh 2 27. 4 5 2 1 5 ln 5 29. 2y4
31. 2e 21 2 6e 25 33. 1 2 ln 2 2 1 2
35. 32 5 sln 2d2 2 64 62
25 ln 2 1 125
37. 2sx e sx 2 2e sx 1 C 39. 2 1 2 2 y4
41. 1 2 sx 2 2 1d lns1 1 xd 2 1 4 x 2 1 1 2 x 1 3 4 1 C
43. 2 1 2 xe22x 2 1 4 e22x 1 C 1
15. 9 8 17. s50 1 28yd°F < 59°F 19. 6 kgym
21. About 4056 million (or 4 billion) people
23. 5ys4d < 0.4 L
Chapter 6 Review • page 466
Exercises
1. 8 3 3. 7 12 5. 4 3 1 4y 7. 64y15 9. 1656y5
11. 4 3 s2ah 1 h 2 d 3y2 13. y y3
2y3 xdscos2 x 2 1 4d dx
15. (a) 2y15 (b) y6 (c) 8y15
17. (a) 0.38 (b) 0.87
19. Solid obtained by rotating the region 0 < y < cos x,
0 < x < y2 about the y-axis
21. Solid obtained by rotating the region 0 < x < ,
0 < y < 2 2 sin x about the x-axis
23. 36 25. 125
3 s3 m 3 27. 3.2 J
29. (a) 8000y3 < 8378 ft-lb (b) 2.1 ft
31. 4y 33. f sxd
_1
45. 1 3 x 2 s1 1 x 2 d 3y2 2 2 15 s1 1 x 2 d 5y2 1 C
_2
F
f
47. (b) 2 1 4 cos x sin3 ms80646-1 x 1 3 8 x 2 3 16 sin 2x 1 C
6et 7.1.41
49. (b) 2 3 , 8 15 8.13.06
55. xfsln xd 3 2 3sln xd 2 1 6 ln x 2 6g 1 C
57. 16 3 ln 2 2 29 9 59. 21.75119, 1.17210; 3.99926
61. 4 2 8y 63. 2e
65. (a) 2(2 ln 2 2 3 4) (b) 2fsln 2d 2 2 2 ln 2 1 1g
67. x Ssxd 1 1 cos( 1 2 x 2 ) 1 C
69. 2 2 e 2t st 2 1 2t 1 2d m 71. 2
4
_4
_1
2
f
F
3
Problems PLUs • page 468
1. (a) f std − 3t 2 (b) f sxd − s2xy 3. 32
27
5. (b) 0.2261 (c) 0.6736 m
(d) (i) 1ys105d < 0.003 inys (ii) 370y3 s < 6.5 min
9. y − 32 9 x 2
11. (a) V − y h f f 0 sydg2 dy
(c) f syd − skAysCd y 1y4 . Advantage: the markings on the
container are equally spaced.
13. b − 2a 15. B − 16A
Exercises 7.2 • page 484
1. 1 3 sin3 x 2 1 5 sin5 x 1 C 3.
1
120
5. 2 1 14 cos7 s2td 1 1 5 cos5 s2td 2 1 6 cos3 s2td 1 C
7. y4 9. 3y8 11. y16
13. 2 7 scos d 7y2 2 2 3 scos d3y2 1 C
15. ln | sin x | 2 1 2 sin2 x 1 C 17. 1 2 sin4 x 1 C
19. 1 4 t 2 2 1 4 t sin 2t 2 1 8 cos 2t 1 C 21. 1 3 sec3 x 1 C
23. tan x 2 x 1 C 25. 1 9 tan9 x 1 2 7 tan 7 x 1 1 5 tan5 x 1 C
27. 1 3 sec3 x 2 sec x 1 C 29. 1 8 tan8 x 1 1 3 tan6 x 1 1 4 tan4 x 1 C
31. 1 4 sec4 x 2 tan 2 x 1 ln | sec x | 1 C
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