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(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) S 8 show that k=1 1 (4k³ - k)² Find each of the following with justification. * f(x) sin x dr. k=1 2 4k³ k sin k.x. 5T 12 (ii) [**f'(x) cos(3x) dr. (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 g(w) = f(w)f(w + 1), g(t) = f(r)e¯¹7 f(t - 7)dr.
Please answer it in 10 hours Don't copy others answer Please write it clearly,then I'll give you upvote
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