a) Let v_n(x) = 2nx/ 1+ n^2x^2 What does the sequence v_n(x) converge to as n → [infinity]? Does the sequence converge pointwise? Uniformly? Justify your answer. b) Compute the Fourier series of f(x) = x on the interval [-π,π]. Write down explicitly to what function the Fourier series converges, draw the function, and justify the convergence by stating the appropriate theorem.