\begin{frame} \frametitle{L'Hospital's Rule} \begin{block}{} A limit of the form \begin{talign} \lim_{x \to a} \frac{f(x)}{g(x)} \end{talign} where both \begin{talign} \lim_{x \to a} f(x) = \pm\infty &&\text{and}&& \lim_{x \to a} g(x) = \pm\infty \end{talign} is called \emph{indeterminate form of type $\frac{\infty}{\infty}$}. \end{block} \pause Often helps to divide by highest power of $x$ in the denominator: \begin{talign} \lim_{x\to \infty} \frac{x^2 - 1}{2x^2 + 1} \mpause[1]{= \lim_{x\to \infty} \frac{1 - \frac{1}{x^2}}{2 + \frac{1}{x^2}} } \mpause[2]{ = \frac{1}{2} } \end{talign} \pause\pause\pause But not for examples like: \begin{exampleblock}{} \begin{talign} \lim_{x\to \infty} \frac{\ln x}{x-1} \end{talign} \end{exampleblock} \end{frame}