Great ideas, was trying for a solution without l'Hôpital but of course both solutions are great. Thanks everyone.
Matt Gironda Science Park HS, Newark, NJ
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-----Original Message----- From: Louis Talman <firstname.lastname@example.org> Date: Thu, 30 Dec 2010 13:31:17 To: AP Calculus<email@example.com> Reply-To: Louis Talman <firstname.lastname@example.org>Cc: Louis Talman<email@example.com>; AP Calculus<firstname.lastname@example.org> Subject: Re: [ap-calculus] Limit Problem driving me nuts!!
On Dec 30, 2010, at 11:38 AM, Douglas J Kuhlmann wrote:
> Use L'Hospital's rule twice: The original problem looks like 0/0 for a limit. L'H says this limit equal > lim(x->1)[(-1+1/x)/(-pi*sin(pi*x)] but this also 0/0. Use L'H on this to get lim(x->1)[(-1/x^2)/(-pi^2*cos(pi*x)] and you get the answer your CAS is giving you.
Alternately, replace both numerator and denominator with, say, 4th order Taylor expansions about x = 1.
--Lou Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver