Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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


    User Avatar
    Science Advisor

    Not that hard though, e.g.
    [tex]x\mapsto x^{1/3}[/tex]
    is not Lipschitz on any nhbd of zero.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Locally Lipschitz
  1. Locally Lipschitz (Replies: 1)

  2. Lipschitz functions (Replies: 1)

  3. Lipschitz function (Replies: 1)