Answer Happy

Please answer it as soon as possible, it’s emergency!!!
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Or you can type the answer, but I need correct and full answer,I mean the format.
(a) Let f: R→ R be a continuously differentiable periodic function of period 27. Given that the Fourier series of f(x) is Moreover, (i) [ f(x) sin x dr. (ii) i) [* f'(x) cos(3x) dx. 1 (4k³ - k)² Find each of the following with justification. k=1 show that + 8 k=1 g(t) = 2 4k-3- k sin kx. 57² 12 (b) Let f: R→ R and g: R → R be piecewise differentiable functions that are integrable. Given that the Fourier transform of f is f(w), and the Fourier transform of g is ĝ(w) = f(w)f(w + 1), - 4. = = f(7) e-7 f(t - 7)dr.