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\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) = \pm\infty &&\text{and}&& \lim_{x \to a} g(x) = \pm\infty
    \end{talign} 
    is called \emph{indeterminate form of type $\frac{\infty}{\infty}$}.
  \end{block}
  \pause

  Often helps to divide by highest power of $x$ in the denominator:
  \begin{talign}
    \lim_{x\to \infty} \frac{x^2 - 1}{2x^2 + 1} \mpause[1]{= \lim_{x\to \infty} \frac{1 - \frac{1}{x^2}}{2 + \frac{1}{x^2}} } \mpause[2]{ = \frac{1}{2} }
  \end{talign}
  \pause\pause\pause
  
  But not for examples like:
  \begin{exampleblock}{}
    \begin{talign}
      \lim_{x\to \infty} \frac{\ln x}{x-1}
    \end{talign}
  \end{exampleblock}
\end{frame}