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

Appendix I Answers to Odd-Numbered Exercises A131
17.
z
3
s9y4d(2 2 s3)
51. (a) 1 15 (b) 1 3 (c) 1 45
53. y 1 0 y12z 0
y sy
2sy
f sx, y, zd dx dy dz 55. 2ln 2 57. 0
x
π
6
y
19. y y2
0
y 3 0 y2 0
f sr cos , r sin , zd r dz dr d
21. 312,500y7 23. 1688y15 25. y8
27. (s3 2 1)a 3 y3 29. (a) 10 (b) (0, 0, 2.1)
31. (a) (0, 0, 12) 7 (b) 11Ky960
33. (a) (0, 0, 3 a) 8 (b) 4Ka 5 y15 (K is the density)
35. 1 3 (2 2 s2), (0, 0, 3yf8(2 2 s2)g)
37. (a) Ka 4 hy2 (K is the density) (b) Ka 2 hs3a 2 1 4h 2 dy12
39. 5y6 41. (4s2 2 5)y15 43. 4096y21
45. 47. 136y99
Problems PLUs • page 1065
1. 30 3. 1 2 sin 1 7. (b) 0.90
13. abcS 2 3 9s3D 2 8
Chapter 16
Exercises 16.1 • page 1073
1.
_2
_1
y
2
1
0 1
x
_1
3.
y
Exercises 15.9 • page 1060
1. 26 3. s 5. 2uvw
7. The parallelogram with vertices (0, 0), (6, 3), (12, 1), s6, 22d
9. The region bounded by the line y − 1, the y-axis, and y − sx
11. x − 1 3 sv 2 ud, y − 1 3su 1 2vd is one possible transformation,
where S − hsu, vd | 21 < u < 1, 1 < v < 3j
13. x − u cos v, y − u sin v is one possible transformation,
where S − 5su, vd | 1 < u < s2, 0 < v < y2 6
15. 23 17. 6 19. 2 ln 3
21. (a) 4 3 abc (b) 1.083 3 1012 km 3 (c) 4 15 sa2 1 b 2 dabck
23. 8 5 ln 8 25. 3 2 sin 1 27. e 2 e21
2
cs130101
_2 1.31.092
_2
5.
y
0
x
x
Chapter 15 Review • page 1061
True-False Quiz
1. True 3. True 5. True 7. True 9. False
Exercises
1. <64.0 3. 4e 2 2 4e 1 3 5. 1 2 sin 1 7. 2 3
9. y 0 y4 2
f sr cos , r sin d r dr d
11. (s3, 3, 2), s4, y3, y3d
13. (2s2, 2s2, 4s3), (4, y4, 4s3)
15. (a) r 2 1 z 2 − 4, − 2 (b) r − 2, sin − 2
17. The region inside the loop of the four-leaved rose r − sin 2
in the first quadrant
19. 1 2 sin 1 21. 1 2 e 6 2 7 2 23. 1 4 ln 2 25. 8
27. 81y5 29. 81 64
2 31. y96 33. 15
35. 176 37. 2 3 39. 2ma 3 y9
41. (a) 1 4 (b) ( 1 3 , 8 15 )
(c) I x − 1 12 , Iy − 1 24 ; y − 1ys3, x − 1ys6
43. (a) s0, 0, hy4d (b) a 5 hy15
45. ln(s2 1 s3) 1 s2y3 47. 486
5
49. 0.0512
7.
z
x
y
9.
z
x
11. IV 13. I 15. IV 17. III
19. 4.5
The line y − 2x
4.5 4.5
4.5
y
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