1. 15x

2. 3. (a) (6 points) (b) (4 points) (i) at = (a) (6 points) 1, Compute the Fourier series of f (x) = Sketch the Fourier series for 3 < x < 3. To what value does the series converge 3? (ii) at = 8? Compute the Fourier sine series of f(x) = cos:r , x G [0, r]. Sketch the Fourier sine series on the interval [2m, 27]. To what value does the series converge at x = O? (b) (4 points) What is the Fourier cosine series of f(.r,) = cos:r , e [O, n]? Include the domain of the series in your answer. [Hint: You shouldn't need to do a calculation for this.)