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\begin{frame}
  \frametitle{Infinite Limits: Vertical Asymptotes}
  
  \begin{block}{}
    The line $x = a$ is a \emph{vertical asymptote} of a function $f$
    if at least one of the following statements is true:
    \begin{talign}
      \lim_{x\to a} f(x) &= \infty &
      \lim_{x\to a^-} f(x) &= \infty &
      \lim_{x\to a^+} f(x) &= \infty\\
      \lim_{x\to a} f(x) &= -\infty &
      \lim_{x\to a^-} f(x) &= -\infty &
      \lim_{x\to a^+} f(x) &= -\infty
    \end{talign}
  \end{block}
  \medskip
  
  \begin{center}
    \scalebox{.6}{
    \begin{tikzpicture}[default]
      \diagram{-2}{5}{-.5}{4}{0}
      \diagramannotatez
      \draw[cblue,ultra thick] plot[smooth,domain=-2:1.5,samples=20] function{1/((x-2)**2)-3/(x**2 + 2)+0.7};
      \draw[cblue,ultra thick] plot[smooth,domain=2.5:5,samples=20] function{1/((x-2)**2)} node [above] {$f(x)$};
      \node [anchor=north,inner sep=1mm] at (2cm,0cm) {$a$};
      \draw [dashed,cred] (2cm,0cm) -- (2cm,4cm);
    \end{tikzpicture}
    }
  \end{center}
\end{frame}