Question

I know we use l'hopital for inf/inf and 0/0, what are the other cases?

Answer 1

http://tutorial.math.lamar.edu/Classes/CalcI/LHospitalsRule.aspx

There are some things you can put in that form also that aren't already in that form
like for example say we have
\[\lim_{x \rightarrow 0}(\sin(x))^{-x}=\lim_{x \rightarrow 0}e^{-x \ln( \sin(x))}=e^{{\lim_{x \rightarrow 0} \frac{\ln(\sin(x))}{\frac{-1}{x}}}}\]
like this wasn't originally in one of the forms you mentioned but now we do have a form in the limit we can use hospital on now
\[=e^{\lim_{x \rightarrow 0} \frac{\cot(x)}{\frac{-1}{x^2}}}=e^ {\lim_{x \rightarrow 0} -x^2 \cot(x)}=e^{\lim_{x \rightarrow 0} \frac{-x^2}{\tan(x)}}\]
so now we have 0/0 we can use l'hosptal again
\[=e^{ \lim_{x \rightarrow 0}\frac{-2x}{\sec^2(x)}}=e^\frac{0}{1^2}=e^0=1 \]

Answer 2

thank you!

Answer 3

np i hope paul's notes were helpful and my example
if you can rewrite the problem where you have 0/0 or pm inf/pm inf
then you can use l'hosptital <--however you spell it

Answer 4

right.. thanks