Let f(x) = |x|, - x, and let (x) ~ /2 + [an cos nx +...

  

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Let f(x) = |x|, - x, and let (x) ~ /2 + [an cos nx + b sin nx] n=1 denote the Fourier series of f. (a) Determine the coefficients an and bn. (b) Prove that the series 1 nan sin nx converges for everyx. (c) For each real x, we set g(x): g on the interval [-2, 2]. = -1 nan sin nx. Sketch the graph of 1 (d) Calculate n=1 (2n-1)2 and n=1 (2n-1) Let f(x) = |x|, - x, and let (x) ~ /2 + [an cos nx + b sin nx] n=1 denote the Fourier series of f. (a) Determine the coefficients an and bn. (b) Prove that the series 1 nan sin nx converges for everyx. (c) For each real x, we set g(x): g on the interval [-2, 2]. = -1 nan sin nx. Sketch the graph of 1 (d) Calculate n=1 (2n-1)2 and n=1 (2n-1)