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

Appendix I Answers to Odd-Numbered Exercises A111
Chapter 10 Review • page 689
True-False Quiz
1. False 3. False 5. True 7. False 9. True
Exercises
1. x − y 2 2 8y 1 12 3. y − 1yx
y
y
(0, 6), t=_4
29. Vertical tangent at
( 3 2 a, 61 2s3 a), s23a, 0d;
horizontal tangent at
sa, 0d, (2 1 2 a, 63 2 s3 a)
y
(3a, 0) (a, 0)
0
x
(5, 1),
t=1
5. x − t, y − st ; x − t 4 , y − t 2 ;
x − tan 2 t, y − tan t, 0 < t , y2 6et Ans. 10.R.3
12.07.06
7. (a) 2π
”4, ’
3
O
2π
3
x
(1, 1), ¨=0
(b) (3s2 , 3y4),
(23s2 , 7y4)
x
31. 18 33. s2, 6y3d 35. 1 2s 2 1d
37. 2(5s5 2 1)
39.
2s 2 1 1 2 s4 2 1 1
2
1 lnS 2 1 s4 2 1 1
1 s 2 1 1
D
41. 471,295y1024
43. All curves have the vertical asymptote x − 1. For c , 21, the
curve bulges to the right. At c − 21, the curve is the line x − 1.
For 21 , c , 0, it bulges to the left. At c − 0 there is a cusp at
(0, 0). For c . 0, there is a loop.
45. s61, 0d, s63, 0d 47. s2 25
24 , 3d, s21, 3d
y
2œ„2
(1, 0)
y
(_1, 3)
9.
(22, 2s3 )
6et Ans. 10.r.7a
12.07.06
(2, π/2)
O
(1, π)
(1, 0)
11.
¨= π 6
(1, 0)
49.
53.
3 0 3
x 2
2œ„2
25 1 y 2
9 − 1 51. y 2
x 2 s8y 2 399d2
1 − 1
25 160,801
x
72y5 2 x 2
8y5 − 1
55. r −
4
3 1 cos
57. x − ascot 1 sin cos d, y − as1 1 sin 2 d
Problems PLUs • page 692
0
x
13.
1
(2, π) (2, 0)
O
_1
2
17. r −
cos 1 sin
5et10R09
Ans wer Ar t
8.14.02
21. 2 23. 21
25.
15.
6et Ans. 10.r.11
12.07.06
3π
”_3, ’
2
π
”1, ’
2
3
y=
2
19. 0.75 6et Ans. 10.R.15
12.07.06
r= sin ¨
¨
O
-0.3 1.2
-0.75
1 1 sin t 1 1 cos t 1 sin t
, 27. s 11
1 1 cos t s1 1 cos td 3 8 , 3 4 d
1. lnsy2d 3. f2 3 4 s3 , 3 4 s3 g 3 f21, 2g
Chapter 11
Exercises 11.1 • page 704
Abbreviations: C, convergent; D, divergent
1. (a) A sequence is an ordered list of numbers. It can also be
defined as a function whose domain is the set of positive integers.
(b) The terms a n approach 8 as n becomes large.
(c) The terms a n become large as n becomes large.
3. 2 3 , 4 5 , 8 7, 16 9 , 32
11 5. 1 5 , 2 1
25 , 1
125 , 2 1
625 , 1
3125 7. 1 2 , 1 6 , 1 24 , 1
120 , 1
720
9. 1, 2, 7, 32, 157 11. 2, 2 3 , 2 5 , 2 7, 2 9 13. an − 1ys2nd
15. a n − 23s23d 2 n21 n 2
17. a n − s21d n11
n 1 1
19. 0.4286, 0.4615, 0.4737, 0.4800, 0.4839, 0.4865, 0.4884,
0.4898, 0.4909, 0.4918; yes; 1 2
21. 0.5000, 1.2500, 0.8750, 1.0625, 0.9688, 1.0156, 0.9922,
1.0039, 0.9980, 1.0010; yes; 1
23. 5 25. D 27. 0 29. 1 31. 2
33. D 35. 0 37. 0 39. D 41. 0 43. 0
45. 1 47. e 2 49. ln 2 51. y2 53. D 55. D
57. D 59. y4 61. D 63. 0
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