(a) (b) (c) Consider the function f(x) = |x| over the interval – L≤ x ≤ L. Derive the Fourier sine series over the interval −L ≤ x ≤ L. Derive the Fourier cosine series over the interval −L ≤ x ≤ L. Derive the full periodic series over the interval -L ≤ x ≤ L.
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- Find the Fourier series for the function (x) = x - x², on the interval (- < x < π).(0,π) Continue the f(x) function as an even or odd function and decompose it into a Fourier series. Continue to draw a graph.Express the odd function f(x) (period = 2 with value 1/2 pi (1-x) for 0 <x<2) as a fourier series. Use the result to calculate the series of 1 -1/3 + 1/5 - 1/7...