Mathematic Methods HW Solutions 4

Mathematic Methods HW Solutions 4 - Chapter 1 15.30 (a) T =...

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Chapter 1 4 15.30 (a) T = F (5 /x + x/ 40 - x 3 / 16000 ··· ) (b) T = 1 2 ( F/θ )(1 + θ 2 / 6 + 7 θ 4 / 360 ··· ) 15.31 (a) fnite (b) infnite 16.1 (c) overhang: 2 3 10 100 books needed: 32 228 2 . 7 × 10 8 4 × 10 86 16.4 C, ρ = 0 16.5 D, a n n→ 0 16.6 C, cF. n - 3 / 2 16.7 D, I = 16.8 D, cF. n - 1 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 - x 2 / 2 + x 3 / 2 - 5 x 4 / 12 ··· 16.15 - x 2 / 6 - x 4 / 180 - x 6 / 2835 ··· 16.16 1 - x/ 2 + 3 x 2 / 8 - 11 x 3 / 48 + 19 x 4 / 128 ··· 16.17 1 + x 2 / 2 + x 4 / 4 + 7 x 6 / 48 ··· 16.18 x - x 3 / 3 + x 5 / 5 - x 7 / 7 ··· 16.19 - ( x - π ) + ( x - π ) 3 / 3! - ( x - π ) 5 / 5! ··· 16.20 2 + ( x - 8) / 12 - ( x - 8) 2 / (2 5 · 3 2 ) + 5( x - 8) 3 / (2 8 · 3 4 ) ··· 16.21 e [1 + ( x - 1) + ( x - 1) 2 / 2! + ( x - 1) 3 / 3! ··· ] 16.22 arc tan 1 = π/
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