1. Let f(x) be a function of period 27 such that f(x) = 1 over the interval 0 < x < 2π. a) Sketch a graph of f(x) in the interval 0 < x < 4π. b) Show that the Fourier series for f(x) is 1 1/17 - (sin x + 1 ½ sin 2.x + 1/3 sin 3x + ... 2 c) By giving an appropriate value to x, show that πT = 1 4 - 2. Let f(x) be a function of period 27 such that S(=) = { 1 1 + 3 5 1 + 7 π-x, 0 < x < π 0,π < x < 2π. a) Sketch a graph of f(x) in the interval -2 < x < 2π. b) Show that the Fourier series for f(x) is πT 4 + 2 1 1 COS x + cos 3x + πT 32 52 ½ cos 5.x + ...). 1 + sin x + sin sin 2x + c) By giving an appropriate value to x, show that sin 3x+ 1 1+ 8 1 + + 72