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

A76 Appendix I Answers to Odd-Numbered Exercises
49. y
1
0 1
x
51. The rate at which the number of US $20 bills in circulation is
changing with respect to time; 0.156 billion bills per year
53. 0
Problems PLUs • page 169
1. 2 3 3. 24 5. (a) Does not exist (b) 1
7. a − 1 2 6 1 2 s5 9. 25 11. (b) Yes (c) Yes; no
13. (a) 0 (b) 1 (c) f 9sxd − x 2 1 1
Chapter 3
Exercises 3.1 • page 180
e h 2 1
1. (a) e is the number such that lim − 1.
h l 0 h
(b) 0.99, 1.03; 2.7 , e , 2.8
3. f 9sxd − 0 5. f 9sxd − 5.2 7. f 9std − 6t 2 2 6t 2 4
9. t9sxd − 2x 2 6x 2 11. t9std − 2 3 2 t 27y4
13. F9srd − 215yr 4 15. R9sad − 18a 1 6
17. S9spd − 1 2 p21y2 2 1 19. y9 − 3e x 2 4 3 x24y3
21. h9sud − 3Au 2 1 2Bu 1 C
23. y9 − 3 2 sx 1 2 2 3
sx 2xsx
25. j9sxd − 2.4x 1.4
27. G9sqd − 22q 22 2 2q 23 29. f 9svd − 2 2 3 v 25y3 2 2e v
31. z9 − 210Ayy 11 1 Be y 33. y − 4x 2 1
35. y − 1 2 x 1 2
37. Tangent: y − 2x 1 2; normal: y − 2 1 2 x 1 2
39. y − 3x 2 1 41. f 9sxd − 4x 3 2 6x 2 1 2x
43. (a) (c) 4x 3 2 9x 2 2 12x 1 7
50
3 5
10
100
3 5
45. f 9sxd − 0.005x 4 2 0.06x 2 , f 99sxd − 0.02x 3 2 0.12x
47. f 9sxd − 2 2 15 4 x21y4 , f 99sxd − 15
16 x25y4
49. (a) vstd − 3t 2 2 3, astd − 6t (b) 12 mys 2
(c) as1d − 6 mys 2
51. 1.718; instantaneous rate of change of the length with respect
to the age at 12 yr
53. (a) V − 5.3yP
(b) 20.00212; instantaneous rate of change of the volume with
respect to the pressure at 258C; m 3 ykPa
55. s22, 21d, s1, 26d 59. y − 3x 2 3, y − 3x 2 7
61. y − 22x 1 3
63. s62, 4d 67. Psxd − x 2 2 x 1 3
40
69. y − 3 16 x 3 2 9 4 x 1 3
71. No
y=ƒ
y
0
(1, 2)
73. (a) Not differentiable at 3 or 23
f 9sxd −H 2x
22x
(b)
y
9
if | x | . 3
if | x | , 3
ƒ
3 0 3 x
x
y
y=fª(x)
ƒ
y
2
1
0
3 3 x
75. y − 2x 2 2 x 77. a − 2 1 2 , b − 2 79. 21 3
81. m − 4, b − 24 83. 1000 85. 3; 1
Exercises 3.2 • page 188
1. 1 2 2x 1 6x 2 2 8x 3 3. f 9sxd − e x s3x 2 1 x 2 5d
5. y9 − 1 2 x
e x 7. t9sxd −
0
10
9. H9sud − 2u 2 1
2
s3 2 4xd
11. F9syd − 5 1 14
y 1 9 2 y 13. y9 − xs2x 3 2 3x 2 2d
4 sx 3 2 1d 2
15. y9 − t 4 2 8t 3 1 6t 2 1 9
st 2 2 4t 1 3d 2
17. y9 − e p s1 1 3 2sp 1 p 1 psp d 19. y9 − 3 2 2ss
2s 5y2
21. f9std − 22t 2 3
3t 2y3 st 2 3d 2
23. f 9sxd − xe x sx 3 1 2e x d
sx 2 1 e x d 2
25. f 9sxd − 2cx
sx 2 1 cd 2
27. sx 3 1 3x 2 1 1de x ; sx 3 1 6x 2 1 6x 1 1de x
xs2 1 2e x 2 xe x d
29.
;
s1 1 e x d 2
2 1 4e x 2 4xe x 2 x 2 e x 1 2e 2x 2 4xe 2x 1 x 2 e 2x
s1 1 e x d 3
31. y − 2 3 x 2 2 3 33. y − 2x; y − 21 2 x
35. (a) y − 1 2 x 1 1 (b) (_1, 0.5)
1
1.5
4 4
0.5
x
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