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: A fun puzzle
Replies: 7   Last Post: Mar 20, 1998 1:46 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Joshua Zucker

Posts: 710
Registered: 12/4/04
A fun puzzle
Posted: Mar 12, 1998 7:34 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Here's a good puzzle to share with your calc BC students as the AP
test approaches...

--Joshua Zucker

From: whuang@ugcs.caltech.edu (Wei-Hwa Huang)
Newsgroups: sci.logic,sci.math,rec.puzzles
Subject: Re: 1 = 0 (proof)
Date: 15 Feb 1998 19:00:33 GMT

Here's another good one that I haven't seen here yet:

Consider the function f(x)=1/(x*lnx), where x>1 (for simplicity) and let's
look at its anti-derivative using integration by parts.

Take u=1/lnx
and dv=(1/x)dx.

Then du=-1/(lnx)^2 * (1/x)dx
and v=lnx.

Therefore, (S is the integral sign)
S 1/(x*lnx) dx = uv - S v*du = 1/lnx * lnx - S [lnx]*[-1/(lnx)^2 * (1/x)dx]
= 1 + S 1/(x*lnx) dx.

Canceling integrals on both sides, we get 0=1.

Q.E.D.

--
Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
---------------------------------------------------------------------------
"...he put a wire in his cap and called himself Marconi."





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.