L'Hôpital's rule

• L'Hôpital's rule: if $\lim_{x \to a}{\frac{f(x)}{g(x)}} =$$\frac{0}{0}$ or $\lim_{x \to a}{\frac{f(x)}{g(x)}} =$$\frac{\infty}{\infty}$ then $\lim_{x \to a}{\frac{f'(x)}{g'(x)}}$

  OR Limit of two functions is equal to the limit of their derivatives, if such limit exists
• Extensions of l'Hôpital's rule:

  $\lim_{x\to\infty}{\frac{lnx}{x}}=$$\frac{\infty}{\infty}=$$\lim_{x\to\infty}{\frac{1/x}{1}}=$$0$