(a) Let f: R → R be a continuously differentiable periodic function of period 27. Given that the Fourier series of f(x)

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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 1 (65.6 KiB) Viewed 52 times

(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) Σ k=1 show that k=1 2 4k³ k sin kæ. 1 (4k³ - k)² Find each of the following with justification. [ f(x) sin x dr. (ii) i) 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 ĝ(w) = f(w)f(w + 1), 57² 12 4. g(t) = f(r)e="* f(t — 7)dr. [5] [5] [5]