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

A132 Appendix I Answers to Odd-Numbered Exercises
21. =f sx, yd − y 2 cossxyd i 1 fxy cossxyd 1 sinsxydg j
x
23. =f sx, y, zd −
sx 2 1 y 2 1 z i 2 y
1
sx 2 1 y 2 1 z j 1 z
2 sx 2 1 y 2 1 z k 2
25. =f sx, yd − sx 2 yd i 1 sy 2 xd j y
27. 4
_4
_4
4
_4 _2
_2
29. III 31. II 33. s2.04, 1.03d
35. (a)
y
(b) y − 1yx, x . 0
4
_4
2
2
4
x
31.
172,704
5,632,705 s2s1 2 e 214 d 33. 2k, s4y, 0d
35. (a) x − s1ymd y C
xsx, y, zd ds,
y − s1ymd y C
ysx, y, zd ds,
z − s1ymd y C
zsx, y, zd ds, where m − y C
sx, y, zd ds
(b) s0, 0, 3d
37. I x − k( 1 2 2 4 3 ), I y − k( 1 2 2 2 3 ) 39. 2 2 41. 7 3
43. (a) 2ma i 1 6mbt j, 0 < t < 1 (b) 2ma 2 1 9 2 mb 2
45. <1.67 3 10 4 ft@lb 47. (b) Yes 51. <22 J
Exercises 16.3 • page 1094
1. 40 3. Not conservative
5. f sx, yd − ye xy 1 K 7. f sx, yd − ye x 1 x sin y 1 K
9. f sx, yd − y 2 sin x 1 x cos y 1 K
11. (b) 16 13. (a) f sx, yd − 1 3 x 3 y 3 (b) 29
15. (a) f sx, y, zd − xyz 1 z 2 (b) 77
17. (a) f sx, y, zd − ye xz (b) 4 19. 4ye
21. It doesn’t matter which curve is chosen.
23. 31 4 25. No 27. Conservative
31. (a) Yes (b) Yes (c) Yes
33. (a) No (b) Yes (c) Yes
Exercises 16.4 • page 1101
y − Cyx
Exercises 16.2 • page 1084
0
x
1. 4 3 s10 3y2 2 1d 3. 1638.4 5. 1 3 6 1 2 7. 5 2
9. s2y3 11. 1 12s14se 6 2 1d 13. 2 5 se 2 1d 15. 35 3
17. (a) Positive (b) Negative 19. 1 20
21. 6 5 2 cos 1 2 sin 1 23. 0.5424 25. 94.8231
27. 3 1 2 3
2.5
2.5 2 .5
2.1
2.5
F{r(1)}
1. 120 3. 2 3 5. 4se3 2 1d 7. 1 3
9. 224 11. 2 16 13. 4
3
1
15. 15 4 2 4144
1125 2 1 7,578,368
253,125 < 0.0779
17. 2 1
12 19. 3 21. (c) 9 2
23. s4ay3, 4ay3d if the region is the portion of the disk
x 2 1 y 2 − a 2 in the first quadrant
27. 0
Exercises 16.5 • page 1109
1. (a) 0 (b) y 2 z 2 1 x 2 z 2 1 x 2 y 2
3. (a) ze x i 1 sxye z 2 yze x d j 2 xe z k (b) yse z 1 e x d
5. (a) 2 sz
s1 1 yd 2 i 2
sx
s1 1 zd 2 j 2
sy
s1 1 xd 2 k
1
(b)
2sx s1 1 zd 1 1
2sy s1 1 xd 1 1
2sz s1 1 yd
7. (a) k2e y cos z, 2e z cos x, 2e x cos yl
(b) e x sin y 1 e y sin z 1 e z sin x
9. (a) Negative (b) curl F − 0
11. (a) Zero (b) curl F points in the negative z-direction.
13. f sx, y, zd − xy 2 z 3 1 K 15. Not conservative
17. f sx, y, zd − xe yz 1 K 19. No
_0.2
F{r(0)}
29. (a) 11 8 2 1ye (b) 0 2.1
1
F”r”
œ„2 ’’
Exercises 16.6 • page 1120
1. P: yes; Q: no
3. Plane through s0, 3, 1d containing vectors k1, 0, 4l, k1, 21, 5l
5. Circular cone with axis the z-axis
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cs13.2.29b