Mathematic Methods HW Solutions 34

# Mathematic Methods HW Solutions 34 - Chapter 7 34 8.20 f(x...

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Unformatted text preview: Chapter 7 34 8.20 f (x) = 2 + 3 ∞ an cos 1 2nπx + 3 ∞ 1 0 , n = 3 k an = −9 , otherwise 8 n2 π 2 9.1 9.2 9.3 9.5 9.7 (a) cos nx + i sin nx x (a) 1 ln |1 − x2 | + 1 ln | 1−x | 2 2 1+ (a) (−x4 − 1) + (x5 + x3 ) ∞ 1 4 sin nx f (x) = π1n an = f (x) 9.8 odd n 2 sin nπ , a0 /2 = 1/2 nπ 2 2 = 1 + π (cos πx − 1 cos 3πx 2 2 3 2 ∞ n+1 (−1) n f (x) = 1 9.9 f (x) = 1 1 +2 12 π π 2 9.10 f (x) = − 4 π 9.11 f (x) = 1 ∞ odd n + 1 5 cos 5πx · · · ) 2 (−1)n cos 2nπx n2 1 cos 2nx n2 1 + 2 ∞ 1 (−1)n cos nx n2 + 1 1 sin nπx n 1 4 9.15 fc (x) = − 2 2π ∞ 1 odd n cos nπx n2 2 fs (x) = π ∞ 1 (−1)n+1 sin nπx n sin nx fc = fp = (1 − cos 2x)/2 n(4 − n2 ) o dd n=1 4 1 1 9.17 fc (x) = (cos πx − cos 3πx + cos 5πx · · · ) π 3 5 ∞ 1 4 fs (x) = fp (x) = sin 2nπx π1n 9.16 fs = 8 π 1 ∞ 1 odd n ∞ 2 9.12 f (x) = − π (b) x sinh x + x cosh x (b) (cos x + x sin x) + (sin x + x cos x) (b) (1 + cosh x) + sinh x ∞ 1 4 nπx 9.6 f (x) = sin π1n l sin 2nx ∞ 2 sinh π π 2nπx bn sin , where 3 − 1 , n = 3 k √ nπ 1 33 bn = − − , n = 3k + 1 nπ 8n2 π 2 √ 1 33 − + 2 2 , n = 3k + 2 nπ 8n π odd n 9.18 Even function: a0 /2 = 1/3, 2 nπ √ 3 nπ {1, 1, 0, −1, −1, 0, and repeat} 1 fc (x) = 1 + π3 (cos πx + 1 cos 2πx − 1 cos 4πx − 1 cos 5πx + 7 cos 7πx 3 3 2 3 4 3 5 3 3 2 1 Odd function: bn = nπ (1 − cos nπ ) = nπ {1, 3, 4, 3, 1, 0, and repeat} 3 1 4 fs (x) = π (sin πx + 3 sin 2πx + 3 sin 3πx 3 2 3 3 3 + 4 sin 4πx + 1 sin 5πx + 1 sin 7πx · · · ) 3 5 3 7 3 an = sin nπ = 3 √ ···) ...
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## This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

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