l'Hospital's rule  Derivative Applications
l'Hospital's rule
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".
Basic concepts:
 Finding limits algebraically  direct substitution
 Limit laws
Lessons
Notes:
Note *l'Hôpital's Rule applies to 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 →$c$} $\frac{f'(x)}{g'(x)}$

1.
Evaluating the limit.
Find: