need solution for all three questions

I. Show that the given functions are orthogonal on the indicated interval. 1. hi(x) = e', fa(x) = re-*- e-*; [0,2] 2. fi(x) = r, f2(x) = cos(2x); [-w/2, "/2] II. Let (,.(x) } be an orthogonal set of functions on [a, b] such that do() = 1 and $1(x) = z. Show that (ar + 3)on(z) da = 0 for n = 2,3, 4, 5, ... and any constants o and B. III. Find the Fourier series expansion of the following functions: 1. f(z) = 2, on 0 S r S 2n 2. f(z) = 0, -1