\begin{frame}
  \frametitle{Infinite Limits: Examples}
  
  \begin{exampleblock}{}
    Find 
    \begin{talign}
      \lim_{x \to 3^-} \frac{2x}{x-3} &&\text{and}&& \lim_{x \to 3^+} \frac{2x}{x-3} 
    \end{talign}
  \end{exampleblock}
  \pause\smallskip
  
  \begin{minipage}{1\textwidth}
  \begin{itemize}
    \item []
    $\lim_{x \to 3^-} \frac{2x}{x-3} = \alt<-2>{?}{-\infty}$ 
    \onslide<-2>{\choice{a} $0$ \choice{b} $1$ \choice{c} $\infty$ \choice{d} $-\infty$}
  \pause\pause
    \item []
    $\lim_{x \to 3^+} \frac{2x}{x-3} = \alt<-4>{?}{\infty}$ 
    \onslide<-4>{\choice{a} $0$ \choice{b} $1$ \choice{c} $\infty$ \choice{d} $-\infty$}
  \end{itemize}
  \end{minipage}
  %
  \hspace*{-.5\textwidth}\begin{minipage}{.49\textwidth}
    \onslide<12->{\scalebox{.6}{
    \begin{tikzpicture}[default,baseline=-1ex]
      \diagram{-1}{5}{-2}{2}{0}
      \diagramannotatez
      \diagramannotatex{1,2,3,4}
      \node at (0,1cm) [anchor=east,inner sep=1mm] {5};
      \draw[cblue,ultra thick] plot[smooth,domain=-1:2.5,samples=20] function{(2*x)/(x-3)/5};
      \draw[cblue,ultra thick] plot[smooth,domain=3.6:5,samples=20] function{(2*x)/(x-3)/5} node [below] {$f(x)$};
      \draw [dashed,cred] (3cm,-2cm) -- (3cm,2cm);
    \end{tikzpicture}
    }}
  \end{minipage}
  \pause\pause\smallskip
    
  If $x$ is close to $3$ and $x < 3$ (approaching from the left), then:
  \begin{itemize}
  \pause 
    \item $2x$ is close to $6$,
  \pause
    \item $x-3$ is a small negative number,
  \pause
    \item and thus $2x/(x-3)$ is a large negative number.
  \end{itemize}
  \pause
  Hence $\lim_{x \to 3^-} \frac{2x}{x-3} = -\infty$.
  \pause\smallskip
  
  Similarly for $x$ close to $3$ and $x > 3$, but now $x-3$ is positive.
%   But now $x-3$ is a small positive number,
%   and hence $\lim_{x \to 3^+} \frac{2x}{x-3} = \infty$.
\end{frame}