The function f(t) = 1 – t² is to be represented by a Fourier series expansion over the finite interval 0 < t < 1. Obtain a suitable

(a) Full-range series expansion;

(b) Half-range sine series expansion;

(c) Half-range cosine series expansion.

Draw graphs of f(t) and of the periodic functions represented by each of the three series for –4 < t < 4.