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bill1158 science forum beginner
Joined: 09 Jul 2006
Posts: 12

Posted: Tue Jul 18, 2006 10:30 pm Post subject:
about uni. continuous proof



in proving uniform continuity, how do we choose the parameter d? any
helpful clues? 

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Lynn Kurtz science forum Guru
Joined: 02 May 2005
Posts: 603

Posted: Tue Jul 18, 2006 10:51 pm Post subject:
Re: about uni. continuous proof



On 18 Jul 2006 15:30:02 0700, "bill" <bilgiaslankurt@gmail.com>
wrote:
Quote:  in proving uniform continuity, how do we choose the parameter d? any
helpful clues?

Your most helpful clues are likely to be in your textbook examples.
Given e > 0 you have to find a d, usually expressed in terms of e such
that:
 f(x)  f(y)  < e when x  y < e.
How you do that depends on the form of the function f(x) you are
dealing with. One common method involves using the mean value theorem
if you have the right conditions. If f' is continuous and  f'(x)  <
M on your domain you can use the MVT to write:
 f(x)  f(y)  < M  x  y 
which will be less than e if  x  y  < e / M
Lynn 

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