Let f(x) = x.
(a) Find all of the Fourier coefficients of f.
(b) Find Pₙ for N = 1, 2, 3, 4, and 5.
(c) Using technology, create a graph of f(x) and P₁(x) on the same set of axes, then graph f(x) and P₂(x) on the same set of axes, and so on, until you have five sets of axes, each with the graph of f and the graph of Pₙ for N = 1, 2, 3, 4, and 5.