Is f(x)=x*sin(x) uniformly continuous? justify.

please help.

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- Jul 13th 2009, 11:12 AMKat-Mhelp
Is f(x)=x*sin(x) uniformly continuous? justify.

please help. - Jul 13th 2009, 06:03 PMpickslides
Here's my adhoc attempt, please trump in anybody...

is uniformly continuous

is uniformly continuous

therefore is also uniformly continuous - Jul 13th 2009, 06:42 PMKrizalid
You're wrong.

Product of two uniformly continuous functions is not uniformly continuous.

Cheap example: is uniformly continuous and is not uniformly continuous.

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is also uniformly continuous. (Actually Lipschitz.) - Jul 13th 2009, 06:53 PMJose27
- Jul 13th 2009, 06:54 PMKrizalid
No, I was giving another example about another uniformly continuous function.

- Jul 13th 2009, 08:09 PMpickslides
Good point Krizalid, also if you graph the function you can see it is not uniformly continuous.