\begin{frame} \frametitle{L'Hospital's Rule} \begin{block}{} A limit of the form \begin{talign} \lim_{x \to a} (f(x)g(x)) \end{talign} where \begin{talign} \lim_{x \to a} f(x) = 0 &&\text{and}&& \lim_{x \to a} g(x) = \pm\infty \end{talign} is called \emph{indeterminate form of type $0\cdot \infty$}. \end{block} \pause\medskip We then rewrite the limit as: \begin{talign} \lim_{x \to a} (f(x)g(x)) = \lim_{x \to a} \frac{f(x)}{1/g(x)} \end{talign} an indeterminate form of type $\frac{0}{0}$\pause, or as \begin{talign} \lim_{x \to a} (f(x)g(x)) = \lim_{x \to a} \frac{g(x)}{1/f(x)} \end{talign} an indeterminate form of type $\frac{\infty}{\infty}$. \end{frame}