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Re: [apcalculus] Limit Problem driving me nuts!!
Posted:
Dec 30, 2010 6:48 PM


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 Sent from my Verizon Wireless BlackBerry
Original Message From: Louis Talman <talmanl@gmail.com> Date: Thu, 30 Dec 2010 13:31:17 To: AP Calculus<apcalculus@lyris.collegeboard.com> ReplyTo: Louis Talman <talmanl@gmail.com>Cc: Louis Talman<talmanl@gmail.com>; AP Calculus<apcalculus@lyris.collegeboard.com> Subject: Re: [apcalculus] 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
<http://rowdy.mscd.edu/%7Etalmanl>
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