how to show sinx uni converges

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October 26th 2008, 05:12 AM
szpengchao

how to show sinx uni converges

$y_{n}(x)=\sin(x), 0\leq |x| \leq 2\pi n$ and

$y_{n}(x)=0, 2\pi n< |x| <\infty$
October 27th 2008, 02:42 AM
CaptainBlack

Quote:

Originally Posted by szpengchao

$y_{n}(x)=\sin(x), 0\leq |x| \leq 2\pi n$ and

$y_{n}(x)=0, 2\pi n< |x| <\infty$

$y_n(x)$ converges pointwise to $\sin(x)$ ,but for all $n$ there exists $x_n$ such that $|y_n(x_n)-\sin(x_n)|=1$ .

CB

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