Re: [math-fun] Riddle about repeated operations (SPOILER)
Q. What do you get when you differentiate sin x with respect to x a hundred times? A. You get cos x every time. :-) Jim Propp P.S. The chain of musings that led me to this riddle started with the literal inaccuracy of the way English speakers describe m times n as what you get when you "add m to itself n times". This is wrong in two ways: we actually add n-1 times, not n times, and what we add m to is not "itself" (except the first time) but rather the running total of all the m's previously added.
Groan.
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun- bounces@mailman.xmission.com] On Behalf Of James Propp Sent: Saturday, October 12, 2013 10:15 PM To: math-fun Subject: Re: [math-fun] Riddle about repeated operations (SPOILER)
Q. What do you get when you differentiate sin x with respect to x a hundred times?
A. You get cos x every time. :-)
Jim Propp
P.S. The chain of musings that led me to this riddle started with the literal inaccuracy of the way English speakers describe m times n as what you get when you "add m to itself n times". This is wrong in two ways: we actually add n-1 times, not n times, and what we add m to is not "itself" (except the first time) but rather the running total of all the m's previously added. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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James Propp