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

Appendix I Answers to Odd-Numbered Exercises A107
41. x − a cos , y − b sin ; sx 2 ya 2 d 1 sy 2 yb 2 d − 1, ellipse
43. y
2a
25. y − x, y − 2x
y
O
45. (a) Two points of intersection
4
(b) One collision point at s23, 0d
when t − 3y2
(c) There are still two intersection
6 6 points, but no collision point.
4
47. For c − 0, there is a cusp; for c . 0, there is a loop whose
size increases as c increases.
3
_1
0
0 1.5
1
x
1
1
2
0 1.5
0
x
27. (a) d sin ysr 2 d cos d 29. s4,0d 31. ab
33. 24 5 35. 2r 2 1 d 2 37. y 2 0 s2 1 2e22t dt < 3.1416
39. y 4
s5 2 4 cos t dt < 26.7298 41. 4s2 2 2
0
43. 1 2 s2 1 1 2 ln(1 1 s2 )
45. s2 se 2 1d 8
25 2.5
0
47. 16.7102 1.4
_3
_1
49. The curves roughly follow the line y − x, and they start
having loops when a is between 1.4 and 1.6 smore precisely,
when a . s2 ). The loops increase in size as a increases.
51. As n increases, the number of oscillations increases;
a and b determine the width and height.
Exercises 10.2 • page 655
1. 1 2 s1 1 td3y2 3. y − 2x 5. y − x 1 2
7. y − 2x 1 1
9. y − 3x 1 3 5
_2.1
49. 612.3053 51. 6s2, s2
55. (a) 15
_1.4
15 15
2.1
t [ f0, 4g
(0, 3)
11.
15.
_2
3
0
2t 1 1
, 2 1
2t 4t , t , 0 13. 3 e22t s1 2 td, e 23t s2t 2 3d, t . 3 2
t 1 1
t 2 1 , 22t
st 2 1d , 0 , t , 1
3
17. Horizontal at s0, 23d, vertical at s62, 22d
19. Horizontal at s 1 2 , 21d and s21 2 , 1d, no vertical
21. s0.6, 2d; (5 ? 6 26y5 , e 6 )
21y5
23. 7.5
15
(b) 294
57. y y2
0
2t cos t st 2 1 1 dt < 4.7394
59. y 1 0 2e2t s1 1 2e t 1 e 2t 1 e 22t dt < 10.6705
61.
2
1215 (247s3 1 64) 63. 6 5 a 2
65. 24 5 (949s26 1 1) 71. 1 4
Exercises 10.3 • page 666
1. (a)
O
π
”1, 4 ’
π
4
(b)
3π
2
3π
”_2, 2 ’
O
8.5 3
1
s1, 9y4d, s21, 5y4d s2, y2d, s22, 7y2d
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