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buzzmath

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## Homework Statement

1. f is a function defined on the interval -a<x<a and has Fourier coefficients an=0 bn=1/n^(1/2) what can you say about the integral from -a to a of f^2(x)dx?

2. Show that as n goes to infinity the Fourier sine coefficients of the function f(x)=1/x -pi<x<pi tend to a nonzero constant. Use the fact that the integral from 0 to infinity of sin(t)/t dt=pi/2

## Homework Equations

## The Attempt at a Solution

1. Persevals equality says 1/a * integral from -a to a of f^2(x)dx = 2a0^2 + susm n=1 to infinity of an^2 + bn^2 so I was thinking that since to a's are zero that we could just say that f^2(x) converges to the sum of the b's but the book says the answer is f^2(x) doesn't converge since sum n=1 to infinity of (|an|+|bn|) is infinity but the a's are zero and bn = 1/n^(1/2) I thought these bn's would go to zero not infinity. What am I doing wrong?

2. f I was just going to compute the bn's from the integral directly and show that as n goes to infinity they go to a nonzero constant but I'm not sure how I would do this problem with the integral given. How does an integral from 0 to infinity come into this problem?

thanks