Results 1 to 2 of 2

Math Help - Lipschitz Continuity

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    7

    Lipschitz Continuity

    I'm having a bit of trouble with the following problems. Any help would be greatly appreciated.

    Are the following functions Lipschitz continuous near 0? If yes, find a Lipschitz constant for some interval containing 0.

    a) f(x) = 1/(1-x^2)

    For this one, I think it's Lipschitz near 0. I have
    |f(x)-f(y)| = [(x+y)/(1-x^2)*(1-y^2)] * (x-y)

    I'm not sure how to find the constant, though.

    b) f(x) = x^2 sin(1/x)

    I don't think this one is Lipschitz near 0, but I don't know how to show it.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jun 2009
    Posts
    113
    If you show that both functions admit a continuous derivative in a closed interval containing 0, then you only have to apply the Mean Value Theorem to find such a constant.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Lipschitz continuity
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 14th 2011, 05:46 AM
  2. proof involving lipschitz and uniformly continuity. is it correct?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 9th 2011, 10:23 AM
  3. Proof involving Lipschitz continuity with constant L
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 30th 2010, 11:21 PM
  4. Lipschitz Continuity
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 22nd 2010, 05:34 PM
  5. Lipschitz continuity
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: November 24th 2009, 12:41 PM

Search Tags


/mathhelpforum @mathhelpforum