Let f (x) = x sin(x) for x . (a) Write the Fourier series

Chapter 13, Problem 13.34

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Let f (x) = x sin(x) for x . (a) Write the Fourier series for f on [,] (b) Show that this series can be differentiated term by term and use this fact to obtain the Fourier expansion of sin(x) + x cos(x) on [,]. (c) Write the Fourier series for sin(x) + x cos(x) on [,] and compare this result with that of (b).

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