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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: $\lim_{x\to a}\,(x\,-\,a)$ doesn't need l'Hôpital's rule. The limit already used l'Hôpital's rule for $\lim_{x\to a}\,\frac{\frac{1}{2}(x\,-\,a)^2}{x\,-\,a}\,\text{.}$ Therefore $\lim_{x\to a}\,\frac{\frac{1}{2}(x\,-\,a)^2}{x\,-\,a}\,=\,0\text{.}$
 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 $\lim_{x\to \infty}\frac{e^{-x}}{e^{-x}}$ 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 $\frac{e^{-x}}{e^{-x}}$. 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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