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Locally Lipschitz

  1. Feb 20, 2008 #1
    Would a trig function like [tex]tan \left(x\right)[/tex] be locally Lipschitz?

    How do we know that, if we know that [tex]tan \left(x\right)[/tex] is not continuously differentiable?
     
    Last edited: Feb 20, 2008
  2. jcsd
  3. Feb 20, 2008 #2

    quasar987

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    tan(x) is continuously differentiable everywhere where it is defined.

    And following my geometrical intuition, I would say that it is locally lip****z, and that you would have to try hard to find a function that is continuous but not locally lipschitz!
     
  4. Feb 1, 2011 #3

    Landau

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    Not that hard though, e.g.
    [tex][-1,1]\to\mathbb{R}[/tex]
    [tex]x\mapsto x^{1/3}[/tex]
    is not Lipschitz on any nhbd of zero.
     
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