# HW 7 1. (a) Starting from the Fourier series for x2, compute the F...

## Transcribed Text

HW 7 1. (a) Starting from the Fourier series for x2, compute the Fourier series for x3, -II <x<t. (b) What values of x does it converge for? 2. (a) Suppose {ak, bk} are Fourier coefficients of f which is piecewise C1 and periodic of period 2. If {ak,bk} are Fourier coefficients of f', find the relationship between {ak,bk} and {ak,b'k} (b) Conclude that {ak, bk} satisfy a strong convergence condition. (c) What if f is piecewise-C'?? 3.Find the Fourier series for f(x) = |sin(x)|. Use the double-angle formula to show that: </x<t.

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