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



