\begin{frame} \frametitle{L'Hospital's Rule} \begin{exampleblock}{} Find \begin{talign} \lim_{x\to \infty} \frac{\ln x}{\sqrt[3]{x}} \end{talign} \pause We have \begin{talign} \lim_{x\to \infty} \ln x = \infty &&\text{and}&& \lim_{x\to \infty} \sqrt[3]{x} = \infty \end{talign}\pause Hence we can apply l'Hospital's Rule: \pause \begin{talign} \lim_{x\to \infty} \frac{\ln x}{\sqrt[3]{x}} = \mpause[1]{ \lim_{x\to \infty} \frac{\frac{d}{dx} \ln x}{\frac{d}{dx} \sqrt[3]{x}} } \mpause[2]{ = \lim_{x\to \infty} \frac{\left(\frac{1}{x}\right)}{\frac{1}{3}x^{-\frac{2}{3}}} } \mpause[3]{ = \lim_{x\to \infty} \frac{3}{\sqrt[3]{x}} } \mpause[4]{ = 0 } \end{talign} \pause\pause\pause \end{exampleblock} \end{frame}