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Topic: [ap-calculus] Limit Problem driving me nuts!!
Replies: 2   Last Post: Dec 30, 2010 6:48 PM

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 Matt Gironda Posts: 66 Registered: 9/5/09
Re: [ap-calculus] 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<ap-calculus@lyris.collegeboard.com>
Reply-To: Louis Talman <talmanl@gmail.com>Cc: Louis Talman<talmanl@gmail.com>; AP Calculus<ap-calculus@lyris.collegeboard.com>
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

<http://rowdy.mscd.edu/%7Etalmanl>

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Course related websites:
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http://apcentral.collegeboard.com/calculusbc
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