Question 1. The function f(t) is defined as follows f(t)=-4-2t+t²,0 < t < 5. Define f (t), an even periodic extension of f(t) and hence select the name of the appropriate Fourier half-range series representation of f(t). The Fourier representation of f(t) is called: the half-range sine series Enter the following values in the boxes below: · p = f (-4), • q = f (8), • T, the period of f (t). Enter p: Enter q: Enter T:

(a) Sketch the graph of the given function for three periods. (b) Find the Fourier series for the given function.

Question 2 Let f(x) = sin(x) - 2. Compute the Fourier series for f.