\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}