solve :

Consider the function f(x) = e 2x on the interval [0,8] (d) Find the Fourier cosine series of f(x) using term by term differentiation of your Fourier sine series of part (a) (Use the formula in Question 1). (e) Find the Fourier sine series of f(x) using term by term integration of your Fourier cosine series of part (b) and compare your result with the Fourier sine series of part (a). when (a), (b) and formula are the following (a) f(x) = 2nn (16)2 + (nn)2 (1+ (-1)"+1 16)sin nux 8 n=1 1 Co (b) f (x ) = 16 (e16 - 1) - 32 (16)2 + (nm)2 ((-1)" e16 -1)cos nux n=1 8 saisfies: f'(x) = _ T bn, cos ( ) + E- ((-1)"f(L) - f(0)) cos (" ) + 7 (f(L) - f(0)) n=1 n=1