L'Hôpital's Rule

=Theorem= L'Hôpital's rule states that for any two functions, $$f(x), g(x) $$ where $$f'(x)$$ and $$g'(x)$$ exist in the neighborhood of c, $$\lim_{x\rightarrow c} \frac{f'(x)}{g'(x)}$$ exists, and $$f(c) = g(c) = 0 $$ or $$ f(c) = g(c) = \infty $$

$$ \lim_{x\rightarrow c} \frac{f(x)}{g(x)} = \lim_{x\rightarrow c} \frac{f'(x)}{g'(x)} $$