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3. (20 pts.) Consider the function f defined on (0, 2) by 2+1 f(x) = = { 0<x< 1 1<x< 2 (a) Denote by fs the sum of the sine Fourier series of f (on (0,2]). Plot the graph of the function fs for x € (-2, 4), indicating the values at each point in that interval. Compute fs(0) and fs(2). [You do not have to compute the coefficients of the Fourier series.] (b) Denote by fc the sum of the cosine Fourier series of f (on (0,2]). Plot the graph of the function fc for x € (-2, 4], indicating the values at each point in that interval. Compute fc(0) and fc(2). [You do not have to compute the coefficients of the Fourier series.]

Answer 1

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