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

A114 Appendix I Answers to Odd-Numbered Exercises
sln 2d
15. ò
n
x n , R − `
n−0 n!
x
17. ò
2n11
n−0 s2n 1 1d! , R − `
19. 50 1 105sx 2 2d 1 92sx 2 2d 2 1 42sx 2 2d 3 1 10sx 2 2d 4
1 sx 2 2d 5 , R − `
1
21. ln 2 1 ò s21d n11
n−1 n2 sx 2 n 2dn , R − 2
2
23. ò
n e 6
sx 2 3d n , R − `
n−0 n!
s21d
25. ò
n11
n−0 s2n 1 1d! sx 2 d2n11 , R − `
31. 1 2 1 4 x 2 3 ? 7 ? ∙ ∙ ∙ ? s4n 2 5d
ò
x n , R − 1
n−2 4 n ? n!
sn 1 1dsn 1 2d
n
33. ò s21d x n , R − 2
n−0
2 n14
1
35. ò s21d n
n−0 2n 1 1 x 4n12 , R − 1
37. ò s21d n
n−0
2 2n
s2nd! x 2n11 , R − `
1
39. ò s21d n
n−0 2 2n s2nd! x 4n11 , R − `
1
41.
2 x 1 1 ? 3 ? 5 ? ∙ ∙ ∙ ? s2n 2 1d
n
ò s21d x 2n11 , R − 2
n−1
n!2 3n11
22n21
n11
43. ò s21d
n−1 s2nd! x 2n , R − `
1
45. ò s21d n
n−0 s2nd! x 4n , R − `
1.5
T¸=T¡=T=T£
49. 0.99619
51. (a) 1 1 ò
n−1
1 ? 3 ? 5 ? ∙ ∙ ∙ ? s2n 2 1d
2 n n!
1 ? 3 ? 5 ? ∙ ∙ ∙ ? s2n 2 1d
(b) x 1 ò
x 2n11
n−1 s2n 1 1d2 n n!
53. C 1 ò
nD
1
2
n−0S
x 3n11
3n 1 1 , R − 1
1
55. C 1 ò s21d n
n−1 2ns2nd! x 2n , R − `
57. 0.0059 59. 0.40102 61. 1 2 63. 1
120 65. 3 5
67. 1 2 3 2 x 2 1 25
24 x 4 69. 1 1 1 6 x 2 1 7
360 x 4
71. x 2 2 3 x 4 1 23
45 x 6
73. e 2x 4 75. ln 8 5
77. 1ys2 79. e 3 2 1
Exercises 11.11 • page 780
1. (a) T 0sxd − 0, T 1sxd − T 2sxd − x, T 3sxd − T 4sxd − x 2 1 6 x 3 ,
T 5sxd − x 2 1 6 x 3 1 1
120 x 5
_2π
5
_5
T¡=T
T¸
T£=T¢
T∞=Tß
f
2π
x 2n
_1.5
1.5
_1.5
Tˆ=T˜=T¡¸=T¡¡
f
T¢=T∞=Tß=T
(b) x f T 0 T 1 − T 2 T 3 − T 4 T 5
y4 0.7071 0 0.7854 0.7047 0.7071
y2 1 0 1.5708 0.9248 1.0045
0 0 3.1416 22.0261 0.5240
s21d
47. ò
n21
n−1 sn 2 1d! x n , R − `
_3
6
T£
T∞
T¡
f
4
(c) As n increases, T nsxd is a good approximation to f sxd on a
larger and larger interval.
3. e 1 esx 2 1d 1 1 2 esx 2 1d2 1 1 6 esx 2 1d3
12
T¡
T
f
T£
T¢ T∞ Tß
_6
T
T¢
Tß
_1
f
T£
0 2.5
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