Problem #1: Let
f(x) = \begin{cases} 5 & -1 < x < 0 \\ 2x & 0 \le x < 1 \end{cases}
The Fourier series for f(x),
f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} (a_n \cos \frac{n \pi x}{p} + b_n \sin \frac{n \pi x}{p})
is of the form
f(x) = c_0 + \sum_{n=1}^{\infty} (g_1(n,x) + g_2(n,x))
(a) Find the value of $c_0$.
(b) Find the function $g_1(n,x)$.
(c) Find the function $g_2(n,x)$.
Problem #1(a):
Problem #1(b):
Problem #1(c):
Enter your answer symbolically,
as in these examples
Enter your answer as a symbolic
function of x,n, as in these
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Enter your answer as a symbolic
function of x,n, as in these
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