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Math (College Level Mathematics)

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Fourier sin series for f(x) = 1, 0 < x < Pie is given by 1 = 4/n E 1/ (2n-1) times sin (2n-1) x, (0 < x < n).

Using this, find the Fourier sinc series for f(x)= 1, on 0 < x < c where c > 0. Then find the Fourier series for g(x), x > 0 where g(x) = 1, 0 < x < c, -1, c < x < 2c, g (x + 2c) = g(x), g (nc) = 0, n = 1, 2, 3, ...

Finally, sketch the graph of g(x), x > 0. Be sure to justify convergence is the F series to g(x) at every x > 0.

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