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

A78 Appendix I Answers to Odd-Numbered Exercises
57. (a) f 9sxd − 2 2 2x 2
s2 2 x 2
59. ssy2d 1 2n, 3d, ss3y2d 1 2n, 21d, n an integer
61. 24 63. (a) 30 (b) 36
65. (a) 3 4 (b) Does not exist (c) 22 67. 21 6s2
69. (a) F9sxd − e x f 9se x d (b) G9sxd − e f sxd f 9sxd
71. 120 73. 96
77. 22 50 cos 2x 79. vstd − 5 2 coss10td cmys
81. (a) dB − 7 2t
cos (b) 0.16
dt 54 5.4
83. vstd − 2e 21.5t s2 cos 2t 2 1.5 sin 2td
2
0 2
1
s
15
0 2
7
85. (a) 0.0075 smgymLdymin (b) 0.0030 smgymLdymin
87. dvydt is the rate of change of velocity with respect to time;
dvyds is the rate of change of velocity with respect to displacement
89. (a) Q − ab t where a < 100.01244 and b < 0.000045146
(b) 2670.63 mA
91. (b) The factored form 95. (b) 2n cos n21 x sinfsn 1 1dxg
√
41. (a) 4
_2
_3
(b) y − 2x 1 1, y − 1 3 x 1 2
5
Eight; x < 0.42, 1.58
(c) 1 7 1
3s3
43. (6 5 4s3, 6 5 4) 45. sx 0 xya 2 d 2 sy 0yyb 2 d − 1
49. y9 − 2 tan21 x
1 1 x 51. y9 − 1
2
s2x 2 2 x
3
53. F9sxd −
sx 6 2 1 1 sec21 sx 3 d 55. h9std − 0
57. y9 − sin 21 x 59. y9 − sa 2 2 b 2
a 1 b cos x
61. 1 2 x arcsin x
s1 2 x 2
65.
y 67.
x
y
x
Exercises 3.5 • page 215
1. (a) y9 − 9xyy (b) y − 6s9x 2 2 1, y9 − 69xys9x 2 2 1
3. (a) y9 − 2sy ysx (b) y − (1 2 sx ) 2 , y9 − 1 2 1ysx
5. y9 − 2y 2 x
y 2 2x
9. y9 −
7. y9 − 2 2xs2x 2 1 y 2 d
ys2x 2 1 3yd
xsx 1 2yd
2x 2 y 1 4xy 2 1 2y 3 1 x 2
13. y9 − 1 2 8x 3 sx 1 y
8y 3 sx 1 y 2 1
17. y9 − 1 1 x 4 y 2 1 y 2 1 x 4 y 4 2 2xy
x 2 2 2xy 2 2x 5 y 3
y cossxyd 1 sinsx 1 yd
19. y9 − 2
x cossxyd 1 sinsx 1 yd
23. x9 − 22x4 y 1 x 3 2 6xy 2
4x 3 y 2 2 3x 2 y 1 2y 3
2x 1 y sin x
11. y9 −
cos x 2 2y
15. y9 − ysy 2 e xyy d
y 2 2 xe xyy
21. 2 16
13
25. y − 1
2 x
27. y − 3 4 x 2 1 2 29. y − x 1 1 2 31. y − 2 9 13 x 1 40
13
33. (a) y − 9 2 x 2 5 2 (b) 5 (1, 2)
2
35. 21ys4y 3 d 37. cos2 y cos x 1 sin 2 x sin y
cos 3 y
_2
_2
39. 1ye 2
71. (a)
V 3 snb 2 Vd
PV 3 2 n 2 aV 1 2n 3 ab
(b) 24.04 Lyatm
73. (6s3, 0) 75. s21, 21d, s1, 1d 77. (b) 3 2
79. (a) 0 (b) 2 1 2
Exercises 3.6 • page 223
1. The differentiation formula is simplest.
cossln xd
3. f9sxd − 5. f 9sxd − 2 1 x
x
2sin x
7. f 9sxd −
9. t9sxd − 1 s1 1 cos xd ln 10
x 2 2
11. F9std − ln t Sln t cos t 1 2 sin t
t
13. G9syd − 10
2y 1 1 2 y 15. F9ssd − 1
y 2 1 1
s ln s
zS 17. T9szd − 2 D
1
z ln 2 1 ln z
19. y9 − 2x 21. y9 − sec 2 flnsax 1 bdg
1 1 x
23. y9 − s2 1 ln xdy(2sx ); y0 − 2ln xy(4xsx )
25. y9 − tan x; y0 − sec 2 x
2x 2 1 2 sx 2 1d lnsx 2 1d
27. f 9sxd − ;
sx 2 1df1 2 lnsx 2 1dg 2
D
a
ax 1 b
s1, 1 1 ed ø s1 1 e, `d
2sx 2 1d
29. f 9sxd − ; s2`, 0d ø s2, `d 31. 2
xsx 2 2d
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