Please answer all of the part questions as this is one whole given to me. It is crucial for me to solve these properly. An 8r periodic function f (t) is given by: 2, f(t) = {-2t, -4n st < 0 0st < 4n f(t + 8n) = f(t) for all of t. a) i. Sketch the graph of f in the interval [-8T, 127). ii. Is the function even, odd, both or none of the parts? b) Calculate the Fourier coefficients ao, an and bn to f(t), and write down the Fourier series of the function. c) Calculate an approximation to f at the point t = r using the first 5 clauses of the Fourier series: an cos(nwt) + b, sin(nwt) n=1 2n W = T where: d) i. Calculate f(20) and f(-207). ii. What does the Fourier series converge towards in t = T? Compare with the answer in task c). ii. What does the Fourier series converge towards in t = 0? e) Use your answers to calculate what value the row converges towards: 00 2 (-1)" 1) n=1