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

Appendix I Answers to Odd-Numbered Exercises A101
67. 8.6 mi
69. (a) 3.8 (b) 1.7867, 0.000646 (c) n > 30
71. (a) D (b) C
73. 2 75. 3 16 2
Problems PLUs • page 541
1. About 1.85 inches from the center 3. 0
7. f sd − 2y2 11. sb b a 2a d 1ysb2ad e 21 13. 1 8 2 1 12
15. 2 2 sin 21 s2ys5d
Chapter 8
Exercises 8.1 • page 548
1. 4s5 3. 3.8202 5. 3.4467 7. 3.6095
2
9. 243 s82s82 2 1d 11. 59
24 13. 32 3
15. ln(s2 1 1) 17. 3 4 1 1 2 ln 2 19. ln 3 2 1 2
21. s2 1 ln(1 1 s2 ) 23. 10.0556
25. 15.498085; 15.374568 27. 7.094570; 7.118819
29. (a), (b)
L 1 − 4,
L 2 < 6.43,
L 4 < 7.50
(c) y 4 0 s1 1 f4s3 2 xdys3s4 2 xd2y3 dg 2 dx (d) 7.7988
31. s1 1 e 4 2 ln(1 1 s1 1 e 4 ) 1 22s2 1 ln(1 1 s2 )
33. 6
17. a 2 19. 1,230,507 21. 24.145807
23. 1 4
25. 1 6 fln(s10 1 3) 1 3s10g
29. (a) 1 3 a 2 (b) 56
45 s3 a 2
f4 ln(s17 1 4) 2 4 ln(s2 1 1) 2 s17 1 4s2 g
31. (a) 2Fb 2 1 a 2 b sin 21 (sa 2 2 b 2 ya)
sa 2 2 b 2
(b) 2a 2 1 2ab 2
ln a 1 sa 2 2 b 2
sa 2 2 b 2 b
33. y b 2fc 2 f sxdgs1 1 f f a 9sxdg2 dx 35. 4 2 r 2
37. Both equal y b a (e xy2 1 e 2xy2 ) 2 dx.
Exercises 8.3 • page 565
1. (a) 187.5 lbyft 2 (b) 1875 lb (c) 562.5 lb
3. 7000 lb 5. 2.36 3 10 7 N 7. 9.8 3 10 3 N
9. 889 lb 11. 2 3 ah2 13. 5.27 3 10 5 N
15. (a) 314 N (b) 353 N
17. (a) 5.63 3 10 3 lb (b) 5.06 3 10 4 lb
(c) 4.88 3 10 4 lb
(d) 3.03 3 10 5 lb
19. 4148 lb 21. 330; 22
23. 10; 14; s1.4, 1d 25. ( 2 3 , 2 3)
27. S 1
e 2 1 , e 1 1
4
D 29. ( 9
20 , 9 20)
31. S s2 2 4
4(s2 2 1) , 1
4(s2 2 1)D 33. ( 8 5 , 21 2)
35. S
28
3s 1 2d , 10
3s 1 2dD 37. s2 1 5 , 212 35d
41. s0, 1 12 d 45. 1 3 r 2 h 47. S 8 , 8 D
49. 4 2 rR
G
35. ssxd − 2 27 fs1 1 9xd 3y2 2 10s10g 37. 2s2 (s1 1 x 2 1)
41. 209.1 m 43. 29.36 in. 45. 12.4
Exercises 8.2 • page 555
1. (a) (i) y y3
0
2 tan xs1 1 sec 4 x dx
(ii) y y3
0
2xs1 1 sec 4 x dx (b) (i) 10.5017 (ii) 7.9353
3. (a) (i) y 1 2 21 2e2x s1 1 4x 2 e 22x 2 dx
(ii) y 1 2xs1 1 4x 0 2 e 22x 2 dx (b) (i) 11.0753 (ii) 3.9603
5. (a) (i) y 1 2ys1 1 s1 1 3y 0 2 d 2 dy
(ii) y 1 2sy 1 0 y3 ds1 1 s1 1 3y 2 d 2 dy
(b) (i) 8.5302 (ii) 13.5134
1
7. 27 (145s145 2 1) 9. 1 6 (27s27 2 5s5 )
11. s5 1 4 lnS D 1 1 s5 13. 21 3712
2 15. 15
2
Exercises 8.4 • page 572
1. $21,104 3. $140,000; $60,000 5. $407.25
7. $166,666.67 9. (a) 3800 (b) $324,900
11. 3727; $37,753 13. 2 3 (16s2 2 8) < $9.75 million
15. $65,230.48 17. s1 2 kdsb 22k 2 a 22k d
s2 2 kdsb 12k 2 a 12k d
19. 1.19 3 10 24 cm 3 ys 21. 6.59 Lymin 23. 5.77 Lymin
Exercises 8.5 • page 579
1. (a) The probability that a randomly chosen tire will have a
lifetime between 30,000 and 40,000 miles
(b) The probability that a randomly chosen tire will have a
lifetime of at least 25,000 miles
3. (a) f sxd > 0 for all x and y`
2`
5. (a) 1y (b) 1 2
f sxd dx − 1 (b)
17
81
7. (a) f sxd > 0 for all x and y`
f sxd dx − 1 (b) 5
2`
11. (a) 46.5% (b) 15.3% (c) About 4.8 s
13. 59.4% (b) 40 min 15. 44%
17. (a) 0.0668 (b) <5.21% 19. <0.9545
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