Examine the uniform continuity of f : R given by f(x) := on .

I know it's not uniformly continuous but how do I prove that?

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- Nov 15th 2009, 07:08 PMthaopandaProve it's not uniformly continous
Examine the uniform continuity of f : R given by f(x) := on .

I know it's not uniformly continuous but how do I prove that? - Nov 15th 2009, 07:18 PMredsoxfan325
- Nov 15th 2009, 07:24 PMJose27
It is uniformly continous:

By the mean value theorem we have where . Taking the supremum over all and noting that we have that for all and so . Now taking in the definition of unif. cont. the result follows.

Actually you can prove that for a continously diff. function it's equivalent:

1) is bounded

2) There exists such that