\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) = 0 &&\text{and}&& \lim_{x \to a} g(x) = 0
    \end{talign} 
    is called \emph{indeterminate form of type $\frac{0}{0}$}.
  \end{block}
  \pause
  
  Often cancellation of common factors helps:
  \begin{talign}
    \lim_{x\to 1} \frac{x^2 - x}{x^2 - 1} \mpause[1]{= \lim_{x\to 1} \frac{(x-1)x}{(x-1)(x+1)}} \mpause[2]{= \lim_{x\to 1} \frac{x}{x+1}} \mpause[3]{= \frac{1}{2}}
  \end{talign}
  \pause\pause\pause
  
  But not for examples like:
  \begin{exampleblock}{}
    \begin{talign}
      \lim_{x\to 0} \frac{\sin x}{x} &&\text{and}&& \lim_{x\to 1} \frac{\ln x}{x-1}
    \end{talign}
  \end{exampleblock}
  
\end{frame}