lipschitz functions

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November 2nd 2009, 06:38 PM
dannyboycurtis

lipschitz functions

I need to show that $f(x)=\sqrt[3]{x}$ and
$g(x)=xsin(\frac{1}{x})$ for $x\in (0,1]$ are NOT Lipschitz.
Im a little lost on how to proceed.
November 2nd 2009, 08:29 PM
dannyboycurtis

is it enough to show that they are not uniformly continuous?
if so Im still not sure how to show that f(x) is not uniformly continous
November 3rd 2009, 04:36 AM
chisigma

Necessary condition for a function to be 'Lipschitz' is that its derivative is bounded in all the interval of definition...

Kind regards

$\chi$ $\sigma$

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