1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lipschitz Continuity

  1. Dec 8, 2006 #1
    1. The problem statement, all variables and given/known data
    Show that Lipschitz continutity imples uniform continuity. In particular show that functions sinx and cosx are uniformly continuous in R.

    3. The attempt at a solution
    I said that if delta=epsilon/k that Lipschitz continuity imples continuity. Now I am stuck as to how to show uniform continuous.
  2. jcsd
  3. Dec 8, 2006 #2


    User Avatar
    Homework Helper

    What are the relevant definitions? Note that Lipschitz continuity is a global property of a function, and uniform continuity is the global version of the local property of ordinary continuity, so it should be straightforward to modify your proof for this case (if it doesn't already apply).
  4. Dec 9, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    As StatusX said, write out the definitions. What is the difference between "continuous" and "uniformly continuous"? (Your "delta=epsilon/k" contains everything you need.)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Lipschitz Continuity
  1. Lipschitz continuity (Replies: 1)

  2. Lipschitz continuous (Replies: 1)