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

Appendix I Answers to Odd-Numbered Exercises A129
13. Type I: D − hsx, yd | 0 < x < 1, 0 < y < xj,
type II: D − hsx, yd | 0 < y < 1, y < x < 1j; 1 3
15. y 1 0 ysx y dy dx 1 2sx y4 1 ysx y dy dx − x22 y2 21 yy12 y dx dy − 9 y 2 4
17. 1 2 s1 2 cos 1d 19. 11 3 21. 0 23. 3 4
25. 31 8 27. 16 128
3 29. 15 31. 1 3
33. 0, 1.213; 0.713 35. 64 3
10 5s2
37. or
3s2 3
39.
z
(1, 0, 0)
x
0
(0, 0, 1)
(0, 1, 0)
41. 13,984,735,616y14,549,535 43. y2
45. y 1 0 y1 f sx, yd dy dx y
x
(0, 1)
(1, 1)
y=x
0
x
47. y 1 0 ycos21 y
0
f sx, yd dx dy
y
1
49. y ln 2
0
y 2 e y f sx, yd dx dy y
0
ln 2
51. 1 6 se 9 2 1d 53. 2 9 (2s2 2 1)
55. 1 3 (2s2 2 1) 57. 1
0
y
y=cos x
or
x=cos _1 y
y=ln x or x=e†
π
2
x=2
y=0
1 2 x
s3
59.
2 < yy s s4 2 x 2 y 2 dA <
61. 3 4 65. 9 67. a 2 b 1 3 2 ab 2 69. a 2 b
Exercises 15.3 • page 1014
1. y 2
0 y5 f sr cos , r sin d r dr d
2
3. y 2
y 1 0
f sr cos , r sin d r dr d
5.
y
3y4
¨= 3π 4
R
¨= π 4
x
9. sy4dscos 1 2 cos 9d
11. sy2ds1 2 e 24 d 13. 3 64 2 15. y12
17.
3 1 s3 19. 625
2
2
3 a 3
25. sy3d(2 2 s2) 27. s8y3d(64 2 24s3)
29. sy4ds1 2 e 24 1
d 31. 120 33. 4.5951
35. 1800 ft 3 37. 2ysa 1 bd 39. 15
16
41. (a) sy4 (b) sy2
7. 1250
3
Exercises 15.4 • page 1024
1. 285 C 3. 42k, (2, 85
9. 1 8 s1 2 3e22 d, S e 2 2 5
e 2 2 3 , 8se 3 2 4d
27se 3 2 3edD
28) 5. 6, ( 3 4 , 3 2) 7. 8 15 k, (0, 4 7)
11. ( 3 8 , 3y16) 13. s0, 45ys14dd
15. s2ay5, 2ay5d if vertex is (0, 0) and sides are along positive
axes
17. 409.2k, 182k, 591.2k
19. 7ka 6 y180, 7ka 6 y180, 7ka 6 y90 if vertex is s0, 0d and sides are
along positive axes
21. bh 3 y3, b 3 hy3; bys3, hys3
23. a 4 y16, a 4 y16; ay2, ay2
25. m − 3y64, sx, yd −S 16384s2
10395 , 0 D,
I x − 5
384 2 4 5
, Iy −
105 384 1 4 5
, I0 −
105 192
27. (a) 1 2 (b) 0.375 (c) 5 48 < 0.1042
29. (b) (i) e 20.2 < 0.8187
(ii) 1 1 e 21.8 2 e 20.8 2 e 21 < 0.3481 (c) 2, 5
31. (a) <0.500 (b) <0.632
33. (a) yy D
kf1 2 1 20 ssx 2 x 0d 2 1 sy 2 y 0d g 2 dA, where D is
the disk with radius 10 mi centered at the center of the city
(b) 200ky3 < 209k, 200(y2 2 8 9 )k < 136k, on the edge
Exercises 15.5 • page 1028
1. 12s35 3. 3s14 5. sy6d(13s13 2 1)
7. sy6d(17s17 2 5s5) 9. s2y3d(2s2 2 1)
11. a 2 s 2 2d 13. 3.6258
15. (a) <1.83 (b) <1.8616
17. 45 8 s14 1 15
16
19. 3.3213 23. sy6d(101s101 2 1)
lnf(11s5 1 3s70)y(3s5 1 s70)g
Exercises 15.6 • page 1037
1. 27 16
4 3. 15 5. 5 3 7. 2 3 9. 27 2 11. 9y8
13. 65
28 15. 8 15 17. 16y3 19. 16 3 21. 8 15
23. (a) y 1 2
0 yx 0 ys12y 0
dz dy dx (b) 1 4 2 1 3
25. 0.985 27.
z
1
_2 _1
0 1 2
x
x
1
0
2
y
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