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

Appendix I Answers to Odd-Numbered Exercises A79
33. y − 3x 2 9 35. cos x 1 1yx 37. 7
4x
39. y9 − sx 2 1 2d 2 sx 4 1 4d
4S
x 2 1 2 1 16x 3
41. y9 −Î S x 2 1 1
x 4 1 1 2x 2 2 2 2x 3
43. y9 − x x s1 1 ln xd
sin x
45. y9 − x
xS sin 1 cos x ln xD
x
47. y9 − scos xd x s2x tan x 1 ln cos xd
49. y9 − stan xd 1yxS sec2 x
x tan x
51. y9 −
2x
x 2 1 y 2 2 2y
2
ln tan x
x 2
x 4 1 4D
x 4 1 1D
D
53. f snd sxd − s21dn21 sn 2 1d!
sx 2 1d n
Exercises 3.7 • page 233
1. (a) 3t 2 2 16t 1 24 (b) 11 ftys (c) Never (d) Always
(e) 72 ft
(f)
(g) 6t 2 16; 210 ftys 2
(h)
t=0
s=0
80
0
_20
a
√
s
t=6
s=72
3. (a) (y2) cos(ty2) (b) 0 ftys
(c) t − 2n 1 1, t a nonnegative integer
(d) 0 , t , 1, 3 , t , 5, 7 , t , 9, and so on
(f)
(h)
2
0
_1
t=0
s=0
√
a
s
t=6
s=1.2
6
t=3
s=1.5
6
s
s
(i) Speeding up when
t . 8 3 ; slowing down when
0 < t , 8 3
(e) 6 ft
(g) (2 2 y4) sin(ty2);
2 2 y4 ftys 2
(i) Speeding up when 1 , t , 2, 3 , t , 4, and 5 , t , 6;
slowing down when 0 , t , 1, 2 , t , 3, and 4 , t , 5
5. (a) Speeding up when 0 , t , 1 or 2 , t , 3;
slowing down when 1 , t , 2
(b) Speeding up when 1 , t , 2 or 3 , t , 4;
slowing down when 0 , t , 1 or 2 , t , 3
7. (a) 4.9 mys; 214.7 mys (b) After 2.5 s (c) 32 5 8 m
(d) <5.08 s (e) <225.3 mys
9. (a) 7.56 mys (b) 6.24 mys; 26.24 mys
11. (a) 30 mm 2 ymm; the rate at which the area is increasing
with respect to side length as x reaches 15 mm
(b) DA < 2x Dx
13. (a) (i) 5 (ii) 4.5 (iii) 4.1
(b) 4 (c) DA < 2r Dr
15. (a) 8 ft 2 yft (b) 16 ft 2 yft (c) 24 ft 2 yft
The rate increases as the radius increases.
17. (a) 6 kgym (b) 12 kgym (c) 18 kgym
At the right end; at the left end
19. (a) 4.75 A (b) 5 A; t − 2 3 s
23. (a) dVydP − 2CyP 2 (b) At the beginning
25. 400s3 t d ln 3; < 6850 bacteriayh
27. (a) 16 millionyyear; 78.5 millionyyear
(b) Pstd − at 3 1 bt 2 1 ct 1 d, where a < 20.0002849,
b < 0.5224331, c < 26.395641, d < 1720.586
(c) P9std − 3at 2 1 2bt 1 c
(d) 14.16 millionyyear (smaller); 71.72 millionyyear (smaller)
(e) f 9std − (1.43653 3 10 9 ) ? (1.01395) t ln 1.01395
(f) 26.25 millionyyear (larger); 60.28 millionyyear (smaller)
(g) P9s85d < 76.24 millionyyear, f 9s85d − 64.61 millionyyear
29. (a) 0.926 cmys; 0.694 cmys; 0
(b) 0; 292.6 scmysdycm; 2185.2 scmysdycm
(c) At the center; at the edge
31. (a) C9sxd − 3 1 0.02x 1 0.0006x 2
(b) $11ypair; the rate at which the cost is changing as the 100th
pair of jeans is being produced; the cost of the 101st pair
(c) $11.07
33. (a) fxp9sxd 2 psxdgyx 2 ; the average productivity increases as
new workers are added.
dt
35.
dc − 3s9c 2 2 8c 1 9c 2 4
; the rate of change
s9c 2 2 8c (3c 1 s9c 2 2 8c )
of duration of dialysis required with respect to the initial urea
concentration
37. 20.2436 Kymin
39. (a) 0 and 0 (b) C − 0
(c) s0, 0d, s500, 50d; it is possible for the species to coexist.
Exercises 3.8 • page 242
1. About 235
3. (a) 100s4.2d t (b) <7409 (c) <10,632 bacteriayh
(d) sln 100dysln 4.2d < 3.2 h
5. (a) 1508 million, 1871 million (b) 2161 million
(c) 3972 million; wars in the first half of century, increased life
expectancy in second half
7. (a) Ce 20.0005t (b) 22000 ln 0.9 < 211 s
9. (a) 100 3 2 2ty30 mg (b) < 9.92 mg (c) <199.3 years
11. <2500 years 13. Yes; 12.5 billion years
15. (a) <1378F (b) <116 min
17. (a) 13.3°C (b) <67.74 min
19. (a) <64.5 kPa (b) <39.9 kPa
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