(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 (151.81 KiB) Viewed 48 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) 8 k=1 show that 2 4k³ - k Find each of the following with justification. **f(x) sin x dr. 1 5r2 (4k³ - k)² 12 sin kæ. = - 4. (ii) [**f'(x) cos(3x) dx. (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)ƒ (w + 1), [5] g(t) = f(r)e-i f(t - 7)dr. [5] [5]