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Unformatted text preview: nx nsin nx n 3 2 x cos nx n 22 sin nx n 3 a n = 2 π ± π f ( x ) cos nx dx = 2 π ² ± π/ 2 f ( x ) cos nx dx + ± π π/ 2 f ( x ) cos nx dx ³ = 2 π ² ± π/ 2 x 2 cos nx dx + ± π π/ 2 π 2 4 cos nx dx ³ = 2 π ² ´ x 2 sin nx n + 2 x cos nx n 22 sin nx n 3 µ ¶ ¶ ¶ ¶ π/ 2 + π 2 4 sin nx n ¶ ¶ ¶ ¶ π π/ 2 ³ = 2 π ´´ π 2 4 n sin nπ 2 + π n 2 cos nπ 22 n 3 sin nπ 2 µ(0 + 00) + π 2 4 ´1 n sin nπ 2 µ = 2 n 2 cos nπ 24 πn 3 sin nπ 2 = (1) n/ 2 2 n 2 n even (1) ( n +1) / 2 4 πn 3 n odd f ( x ) = π 64 π 1 3 cos x + 2 2 2 cos 2 x + 4 π 3 3 cos 3 x2 4 2 cos 4 x4 π 5 3 cos 5 x + 2 6 2 cos 6 x + . . ....
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 Spring '08
 Bellenot
 Math, Fourier Series, Cos, Shawn Ashmore

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