(a) Consider a function f(x) that is even around x = L/2. Show that the odd coefficients (n odd) of the Fourier cosine series of f(x) on 0 ≤ x ≤ L are zero.
(b) Explain the result of part (a) by considering a Fourier cosine series of f(x) on the interval 0 ≤ x ≤ L/2.
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