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

A128 Appendix I Answers to Odd-Numbered Exercises
Chapter 14 Review • page 982
1. hsx, yd
True-False Quiz
1. True 3. False 5. False 7. True 9. False
11. True
Exercises
| y . 2x 2 1j 3. z
y
1
_1
x
x
1
y
_1
59. Maximum f (6s2y3, 1ys3) − 2y(3s3),
minimum f (6s2y3, 21ys3) − 22y(3s3)
61. Maximum 1, minimum 21
63. (63 21y4 , 3 21y4 s2, 63 1y4 ), (63 21y4 , 23 21y4 s2, 63 1y4 )
65. P(2 2 s3), P(3 2 s3)y6, P(2s3 2 3)y3
Problems PLUs • page 985
1. L 2 W 2 , 1 4 L2 W 2 3. (a) x − wy3, base − wy3 (b) Yes
7. s3y2, 3ys2
Chapter 15
5.
y=_x-1
y
3c3 Ans 11.R.1
09.23.04
1 23 4 5
0
x
7.
y
2
1
0
3c3 Ans 11.R.3
09.16.04
1
2
x
Exercises 15.1 • page 999
1. (a) 288 (b) 144 3. (a) 0.990 (b) 1.151
5. U , V , L 7. (a) <248 (b) <15.5
9. 24s2 11. 3 13. 2 1 8y 2 , 3x 1 27x 2
15. 222 17. 5 2 2 e21 19. 18
21. 15 2 ln 2 1 3 2 ln 4 or 21 2 ln 2 23. 6
25. 31
30
27. 2 29. 9 ln 2
31. 1 2 (s3 2 1) 2 1 12 33. 1 2 e26 1 5 2
35.
z
4
9. 2 ca11r07
3
10.28.00
11. (a) <3.5°Cym, 23.0°Cym
3c3 Ans 11.R.5
(b) < 0.35°Cym 09.16.04 by Equation 14.6.9 (Definition 14.6.2 gives
<1.1°Cym.)
(c) 20.25
13. f x − 32xys5y 3 1 2x 2 yd 7 , f y − s16x 2 1 120y 2 ds5y 3 1 2x 2 yd 7
15. F − 2 3
2 1 1 2 lns 2 1 2 d, F 2 −
2 2
2 1 2
17. S u − arctan(vsw ), S v − usw
1 1 v 2 w , Sw − uv
2sw s1 1 v 2 wd
19. f xx − 24x, f xy − 22y − f yx, f yy − 22x
21. f xx − ksk 2 1dx k22 y l z m , f xy − klx k21 y l21 z m − f yx,
f xz − kmx k21 y l z m21 − f zx, f yy − lsl 2 1dx k y l22 z m ,
f yz − lmx k y l21 z m21 − f zy, f zz − msm 2 1dx k y l z m22
25. (a) z − 8x 1 4y 1 1 (b) x 2 1
8
27. (a) 2x 2 2y 2 3z − 3 (b) x 2 2
29. (a) x 1 2y 1 5z − 0
(b) x − 2 1 t, y − 21 1 2t, z − 5t
31. (2, 1 2 , 21), (22, 21 2 , 1)
4
− y 1 2
4
− z 2 1
21
− y 1 1
24 − z 2 1
26
33. 60x 1 24 5 y 1 32 5 z 2 120; 38.656
35. 2xy 3 s1 1 6pd 1 3x 2 y 2 s pe p 1 e p d 1 4z 3 s p cos p 1 sin pd
37. 247, 108
43. k2xe yz 2 , x 2 z 2 e yz 2 , 2x 2 yze yz 2 l 45. 2 4 5
47. s145y2, k4, 9 2 l 49. < 5 8 knotsymi
51. Minimum f s24, 1d − 211
53. Maximum f s1, 1d − 1; saddle points (0, 0), (0, 3), (3, 0)
55. Maximum f s1, 2d − 4, minimum f s2, 4d − 264
57. Maximum f s21, 0d − 2, minima f s1, 61d − 23,
saddle points s21, 61d, s1, 0d
x
1
0
1
y
37. 51 39. 166
27 41. 8 3 43. 64 3
45. 21e 2 57
7etA150223
08/19/10 2
MasterID: ms09696
z
0
0
y
1
1
47. 5 6 49. 0
51. Fubini’s Theorem does not apply. The integrand has an infinite
discontinuity at the origin.
Exercises 15.2 • page 1008
1. 868
3 3. 1 6 se 2 1d 5. 1 3 sin 1
7. 1 4 ln 17 9. 1 2 s1 2 e29 d
11. (a) (b)
y
y
0 x
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D
x
D
0
0 x
12.3.11b
82359