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Let 4 0sx<I f(x) x-1, 1sx<2 Consider the odd periodic extension, of period T 4, of f(x) Sketch the graph of this odd periodic



Let 4 0sx<I f(x) x-1, 1sx<2 Consider the odd periodic extension, of period T 4, of f(x) Sketch the graph of this odd periodic extension of f(x) in the interval [-4, 4] b) Write down the form of the Fourier coefficients and the Fourier series of f(x), but DO NOT compute the coefficients. To what value does the series converge when i) x 0 ii x 2

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(b) Fourier series F (x) = a_0/2 + sigma^infinity_n = 1 [a_n cos n pi x/2 + b_n sin n pi x/2] where a_0 = 2/2 in

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