Lipschitz Continuity

  • #1

Homework Statement


Show that Lipschitz continutity imples uniform continuity. In particular show that functions sinx and cosx are uniformly continuous in R.


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.
 

Answers and Replies

  • #2
StatusX
Homework Helper
2,564
1
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).
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
964
As StatusX said, write out the definitions. What is the difference between "continuous" and "uniformly continuous"? (Your "delta=epsilon/k" contains everything you need.)
 

Related Threads on Lipschitz Continuity

  • Last Post
Replies
1
Views
464
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
889
Replies
5
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
9
Views
3K
Top