# l'Hospital's rule

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###### Topic Notes

Remember that one tricky Limits section that required intense algebraic manipulation to avoid getting 0/0 or infinity/infinity limits? We will now revisit it again, but with the knowledge of derivatives. In this section, we will learn how derivatives enable us to efficiently evaluate the limits of a function using the "L'Hospital's rule".

Note *l'Hôpital's Rule applies to

or

Then according to l'Hôpital's Rule: $\lim$

**2 types**of indeterminate forms:**type $\frac{0}{0}$**(that is, $\lim$_{x →$c$}$f(x)=0$ and $\lim$_{x →$c$}$g(x)=0$)or

**type $\frac{\infty}{\infty}$**(that is, $\lim$_{x →$c$}$f(x)=\pm \infty$ and $\lim$_{x →$c$}$g(x)=\pm \infty$)Then according to l'Hôpital's Rule: $\lim$

_{x →$c$}$\frac{f(x)}{g(x)}=$ $\lim$_{x →$c$}$\frac{f'(x)}{g'(x)}$###### Basic Concepts

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