Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Courses » ap-calculus

Topic: [ap-calculus] Limit Question - Sandwhich Theorem
Replies: 2   Last Post: Aug 24, 2012 4:44 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Dave L. Renfro

Posts: 2,165
Registered: 11/18/05
re:[ap-calculus] Limit Question - Sandwhich Theorem
Posted: Aug 24, 2012 4:44 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Jean Contreras wrote (in part):

http://mathforum.org/kb/message.jspa?messageID=7873988

> Also is the Sandwich theorem only really used with sine
> and cosine? If not does anyone have some other good examples.


Let f be the function defined by f(x) = 0 if x is rational
and f(x) = 1 if x is irrational. Note that f is discontinuous
at every point. In fact, at every point f has neither a left
limit nor a right limit.

Now define the function g by putting g(x) = x*f(x).

Using the Sandwich Theorem, you can show that g is
continuous at x = 0. It's also easy to show that g
is not continuous at every other point, so g has the
property that it's continuous at exactly one point.

Dave L. Renfro
====
Course related websites:
http://apcentral.collegeboard.com/calculusab
http://apcentral.collegeboard.com/calculusbc
---
To search the list archives for previous posts go to
http://lyris.collegeboard.com/read/?forum=ap-calculus
To unsubscribe click here:
http://lyris.collegeboard.com/read/my_forums/
To change your subscription address or other settings click here:
http://lyris.collegeboard.com/read/my_account/edit



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.