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\begin{frame}
  \frametitle{1st Midterm Exam - Review}

  \begin{exampleblock}{}
    Prove or disprove that the following limit exists
    \begin{talign}
      \lim_{x\to 5} \frac{x-5}{|x-5|}
    \end{talign}
    \pause
    For $x < 5$ we have $\frac{x-5}{|x-5|} = -1$. \pause Thus
    \begin{talign}
      \lim_{x\to 5^-} \frac{x-5}{|x-5|}
      &\mpause[1]{= \lim_{x\to 5^-} -1}
      \mpause[2]{= -1}
    \end{talign}
    \pause\pause\pause
    For $x > 5$ we have $\frac{x-5}{|x-5|} = 1$. \pause Thus
    \begin{talign}
      \lim_{x\to 5^+} \frac{x-5}{|x-5|}
      &\mpause[1]{= \lim_{x\to 5^+} 1}
      \mpause[2]{= 1}
    \end{talign}
    \pause\pause\pause\medskip
    
    The limit $\lim_{x\to 5} \frac{x-5}{|x-5|}$ does not exist
    since the left- and the right-limit are different.
  \end{exampleblock}
\end{frame}