EGM4313HW1 - P 482#17 1 2 a0 f x dx x dx 2 0 1 an 1 2 f x...

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P. 482, #17: 0 0 0 2 2 1 3 5 2 4 6 1 1 2 2 1 2 cos cos 2 2 1 cos 1 1 4 4 4 , , , 9 25 0 1 sin 0 4 1 1 cos cos 3 cos 5 2 9 25 n n n a f x dx x dx a f x nx dx x nx dx n n n a a a a a a b f x nx dx f x x x x P. 482, #18: 1 0 1 3 5 2 4 6 1, 0 1/ 2, 0 1 0, 0 1/ 2, 0 2 1 sin 2 2 1 1 1 sin 1 cos 1 1 2 2 2 2 , , , 3 5 0 1 2 1 1 sin sin 3 sin 5 2 3 5 n n n n x x f x x x b nx b nx dx n n n b b b b b b f x x x x
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P. 490, #24: 0, 0 2 1, 2 4 x f x x Fourier Cosine Series: 4 4 0 0 2 4 4 0 2 1 3 5 2 4 6 1 1 1 4 2 2 2 1 cos cos 4 4 2 4 2 sin 2 2 2 2 , , , 3 5 0 1 2 1 3 1 5 cos cos cos 2 4 3 4 5 4 n a f x dx dx n x n x a f x dx dx n n a a a a a a x x x f x Fourier Sine Series: 4 4 0 2 1 2 3 4 5 6 7 8 2 1 sin sin 4 4 2 4 2 cos cos 2 2 2 2 2 2 2 , , , 0, , , , 0, 3 5 3 7 2 1 3 1 5 1 3 sin sin sin sin sin 4 2 3 4 5 4 3 n n x n x b f x dx dx n n n b b b b b b b b x x x x f x 1 7 sin 2 7 4 x x
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Page 494, #16: , / 2 / 2 , / 2 3 / 2 t t r t t t , 2 π -periodic r t is an odd function 0, 0,1,2,3, n a n /2 0 0 /2 2 2 2 sin sin sin 4 sin 2 sin 0 2 sin 1 1,5,9, 2 sin 1 3,7,11, 2 n b r t nt dt t nt dt t nt dt n n n if n even n if n n if n Consider the equation 2 4 sin y cy y nt n and look for particular solutions of the form (method
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