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

please help.

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- Jul 13th 2009, 10:12 AM #1

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- Jul 13th 2009, 05:03 PM #2

- Jul 13th 2009, 05:42 PM #3
You're wrong.

Product of two uniformly continuous functions is not uniformly continuous.

Cheap example: $\displaystyle f(x)=x$ is uniformly continuous and $\displaystyle g(x)=f(x)\cdot f(x)=x^2$ is not uniformly continuous.

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$\displaystyle h(x)=\sin x$ is also uniformly continuous. (Actually Lipschitz.)

- Jul 13th 2009, 05:53 PM #4

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- Jul 13th 2009, 05:54 PM #5

- Jul 13th 2009, 07:09 PM #6