f(x) is a differentiable periodic function of period 2. The Fourier series for its derivative f'(x) is 1 (13) ^nsin (nx). (a) Find the Fourier series for f(x) if (0) = 2. (Hint: geometric series.) (b) Explain why f(x) is infinitely differentiable (i.e. f(x) exists for any positive integer k).