(b) (c) (d) (e) (f) Consider the function f(x) = |x| over the interval – L≤ x ≤ L. Derive the Fourier sine series over the interval −L ≤ x ≤ L. = = L Derive the Fourier cosine series over the interval –L ≤ x ≤ L. Derive the full periodic series over the interval -L ≤ x ≤ L. For each series computed in parts (a) - (c) what is the value at x Which of the series in parts (a) - (c) can be differentiated term by term so that the resulting series converges to the derivative of f(x) with respect to x over the interval -L≤ x ≤ L? Which of the series in parts (a) - (c) can be integrated term by term so that the resulting expression converges to the integral S* f ( x') dx'