Question: A. (6 points) Let f: (-, ) - R be f(I) = r+ 1. (a) Find the Fourier series of f. (b) Let F: R

A. (6 points) Let f: (-", ") - R be f(I) = r+ 1. (a) Find the Fourier series of f. (b) Let F: R - R be the Fourier series of part (a). Find F(#). (Hint: Sketch the graph of F.) (c) Use part (a) to prove that 1 - 091 H -JH (d) Does the Fourier series of part (a) converge uniformly on [-2x, 2x]? Briefly explain

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