This is the cosine series for f(x) = sinx on the interval [0, ]: 1 +...

 

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This is the cosine series for f(x) = sinx on the interval [0, π]: 1 + (−1)n 1-n² NIE 2 2 + ㅠ n=2 cos(nx) (a) Sketch the function whose Fourier series on [-, π] is given above. (The point is to do this without technology.) (b) Find the sine series for f'(x) on [0, 7] without using the Bn formulas, etc. Feel free to put f'(x) and your series into Desmos to check your result. This is the cosine series for f(x) = sinx on the interval [0, π]: 1 + (−1)n 1-n² NIE 2 2 + ㅠ n=2 cos(nx) (a) Sketch the function whose Fourier series on [-, π] is given above. (The point is to do this without technology.) (b) Find the sine series for f'(x) on [0, 7] without using the Bn formulas, etc. Feel free to put f'(x) and your series into Desmos to check your result.

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