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15.30 Chapter (a) T = F (5/x + x/40 x3 /16000 )
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(b) T = 2 (F/)(1 + 2 /6 + 74 /360 )
15.31 (a) nite
(b) innite
16.1 (c) overhang:
2
3
10
100
books needed:
32
228
2.7 108
4 1086
16.4 C, = 0
16.5 D, an 0
16.6 C, cf.
n3/2
1
16.7 D, I =
16.8 D, cf.
n
16.9 1 x < 1
16.10 |x| < 4
16.11 |x| 1
16.12 |x| < 5
16.13 5 < x 1
16.14 1 x2 /2 + x3 /2 5x4 /12
16.15 x2 /6 x4 /180 x6 /2835
16.16 1 x/2 + 3x2 /8 11x3 /48 + 19x4 /128
16.17 1 + x2 /2 + x4 /4 + 7x6 /48
16.18 x x3 /3 + x5 /5 x7 /7
16.19 (x + ) (x )3 /3! (x )5 /5!
16.20 2 + (x 8)/12 (x 8)2 /(25 32 ) + 5(x 8)3 /(28 34 )
16.21 e[1 + (x 1) + (x 1)2 /2! + (x 1)3 /3! ]
16.22 arc tan 1 = /4
16.23 1 (sin )/ = 1
16.24 eln 3 1 = 2
16.25 2
16.26 1/3
16.27 2/3
16.28 1
16.29 6!
16.30 (b) For N = 130, 10.5821 < (1.1) < 10.5868
16.31 (a) 10430 terms. For N = 200, 100.5755 < (1.01) < 100.5803
16.31 (b) 2.66 1086 terms. For N = 15, 1.6905 < S < 1.6952
200
86
16.31 (c) ee = 103.138210 terms. For N = 40, 38.4048 < S < 38.4088
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