Recall the ∞ ∞ {\displaystyle {\frac {\infty }{\infty }}} L'Hopital's Rule: If lim x → a f ( x ) = ∞ , lim x → a g ( x ) = ∞ , {\displaystyle \lim _{x\to a}f(x)=\infty ,\lim _{x\to a}g(x)=\infty ,} and both f {\displaystyle f} and g {\displaystyle g} are differentiable at x = a {\displaystyle x=a} , then
lim x → a f ( x ) g ( x ) = lim x → a f ′ ( x ) g ′ ( x ) . {\displaystyle \lim _{x\to a}{\frac {f(x)}{g(x)}}=\lim _{x\to a}{\frac {f'(x)}{g'(x)}}.}
