Let f be the 4-periodic funtion on R with one period given by if 2x < −1 - 0 f(x) = 1 if - 0 1<<1. if 1 < x < 2 Find the Fourier series of f. Sf(x) = ao + Σαπ ппх ппх an COS + bn sin === 2 2 n=1 1/2 ппх COS +0 2 + ∞ (2sin(npi/2))/(pin) n=1 ппх sin 2 Note: Your coefficients should match the given cos (2) and sin (TI) terms in the above equation. Therefore, do not collapse your coefficients. In particular, do not remove the zero terms and reindex. For what value(s) of x is f(x) equal to its Fourier series Sf(x) on the interval [-2,2]? Give your answer as an interval or union of intervals. x€ (-1,1) For values of a where f(x) Sf(x), evaluate Sf(x). Sf(x) = x

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