\begin{frame}
  \frametitle{L'Hospital's Rule}

  \begin{exampleblock}{}
    Find 
    \begin{talign}
      \lim_{x\to 0} \frac{\sin x}{x}
    \end{talign}
    \pause
    We have
    \begin{talign}
      \lim_{x\to 0} \sin x = 0 &&\text{and}&&
      \lim_{x\to 0} x = 0
    \end{talign}\pause
    Hence we can apply l'Hospital's Rule:
    \pause
    \begin{talign}
      \lim_{x\to 0} \frac{\sin x}{x} = 
      \mpause[1]{ \lim_{x\to 0} \frac{\frac{d}{dx}\sin x}{\frac{d}{dx} x} }
      \mpause[2]{ = \lim_{x\to 0} \frac{\cos x}{1} }
      \mpause[3]{ = 1 }
    \end{talign}\pause
  \end{exampleblock}  

\end{frame}