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

 Messages: [ Previous | Next ]
 Joshua Zucker Posts: 710 Registered: 12/4/04
A fun puzzle
Posted: Mar 12, 1998 7:34 PM

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."

Date Subject Author
3/12/98 Joshua Zucker
3/14/98 Dave Slomer
3/20/98 John Graham
3/20/98 Jerry Uhl
3/14/98 AtlntaMath@aol.com
3/14/98 Alvar J. Garcia
3/15/98 SGold2112
3/18/98 Geoff Hagopian