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June 23rd, 2011, 03:44 AM  #1 
Member Joined: Apr 2011 From: Sri Lanka Posts: 71 Thanks: 1  what are the limit questions whic you can't apply L'hopital'
Can't we apply L'hopital's rule for all the limits questions? I know that it can be used only if it is an undetermined foam. But if it is a determined form, will there be a question to find the limit of? 
June 23rd, 2011, 08:36 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,105 Thanks: 1907 
Not all limits problems involve fractions.

June 23rd, 2011, 04:29 PM  #3 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Example: doesn't need l'Hôpital's rule. The limit already used l'Hôpital's rule for Therefore 
June 23rd, 2011, 04:45 PM  #4 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
The limit can be determined by canceling out the factors x  a. Hence l'Hôpital's rule isn't necessary, but it works. 
June 24th, 2011, 07:21 AM  #5 
Member Joined: Apr 2011 From: Sri Lanka Posts: 71 Thanks: 1  Re: what are the limit questions whic you can't apply L'hopi
Thanks Johnny and skipjack for the answers !!

June 26th, 2011, 06:24 AM  #6 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: what are the limit questions whic you can't apply L'hopi is an example of a "0/0" limit where L'Hopital's rule does not work. No matte how many times you differentiate numerator and denominator separately, you keep getting . If the fraction is a "determined form" then there are two possiblities: the denominator does not go to 0 so you can just evaluate the fraction, or the denominator goes to 0 while the numerator does not and that has no limit. 

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