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

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

\end{frame}