Question 4 (15 marks, C3) (a) Let f : R - R be a continuously differentiable periodic function of period 27. Given that the Fourier series of f(x) is 2 413 - k - sin kx. K=1 Moreover, 1 572 k=1 (41-3 - k)2 4. 12 Find each of the following with justification. [5] (1) f'(x) cos (3x) dx. [5] (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 g ( w ) = f (w) f ( w + 1), show that g (1 ) = / { ( T)e-if (t - T )dr . [5]