This is what I have so far:

3) (40 points) Write a Maple procedure FS which takes inputs of a function f(x) defined on [-, ] and a natural number n, and generates the n-term Fourier series of of f(z), The outputs of FS are the the n-term Fourier series of of f(z) and the graph of the n-term Fourier series on [-3T.3 Apply the procedure to -2(n + x), xe(-r,-/2), x E (-r/2, /2) xe(n/2, ), 2(n-x), for n 10 The input of the procedure are f and n, i.e. the first line of your procedure should be FS:-proc(f,n) The output of the procedure are the Fourier series and its graph, i.e. the last line before end; of your procedure is (assuming fs is the Fourier series) fs,plot(fs,x-3*Pi..3*Pi) FS := proc (f, n) local a0, ai, bi, pf fl, gl, hl,x # piecewise-functions fl piecewise(-Pi x Pi, x): gl := piecewise(-H > x > 0,-Pi, 0 x > 0,-Pi, 0