Expand f(x) = cos x, 0 < x < π, in a pure Fourier "sine" series on (0, π).
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- Expand the function f(x) = X, if 0 < x < 3 6x, if 3 < x < 6 in a half-range (a) sine series; and (b) cosine series. In addition, plot what the two Fourier series converge to.Please Help ASAP!!!How can one find the Fourier series of f(x)=x^3 -(pi^2)*x based on knowing the cosine Fourier series for f(x)=x? I first did it using the x series in sines and integrating it twice, and that comes out easily, but can't understand how to do it starting with the cosines version of f(x)=x, which is given as x =pi/2 + sum [(2[-1^n)-1] cos(nx)/(pi*n^2)]
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