Consider the Fourier expansion 2 k = ∞ f(x) = Σck · sin(ka), k=1 where Ck (-1) 2k+1. Describe the periodic function f(x). Verify that the first Fourier coefficient satisfies C1 = π \^ π xsin (x) dx.

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A: Since you have asked multiple questions, we will solve the first Question for you. If you want any…

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