\begin{frame}
  \frametitle{Limit: Examples}

  \begin{exampleblock}{}
    Guess the value of 
    \begin{talign}
      \lim_{x\to 1} \frac{x-1}{x^2-1}
    \end{talign}
  \end{exampleblock}
  \pause
  \medskip
  
  \begin{minipage}{.43\textwidth}
    \scalebox{.6}{
    \begin{tikzpicture}[default]
      \diagram{-1}{5}{-1}{5}{1}
      \diagramannotate
      \draw[cblue,ultra thick] plot[smooth,domain=-.8:4.5,samples=20] (\x,{(\x-1)/(pow(\x,2)-1)});
  
      \def\x{1}
      \def\y{{.5}}
      \begin{scope}[dashed,cred,ultra thick,inner sep=1mm]
      \draw (\x,\y) -- (\x,0mm);
  %     \draw (\x,\y) -- (-2mm,\y) node [left] {$L$};
      \end{scope}
      \node[exclude={cblue}] at (\x,\y) {};
  %     \node[include={cblue},yshift=-10mm] at (\x,\y) {};
    \end{tikzpicture}
    }
  \end{minipage}
  \begin{minipage}{.56\textwidth}
    \pause
    The function is not defined at $x=1$.\\
    \pause
    (does not matter for the limit)
    \bigskip
    \pause
    
    \begin{minipage}{.49\textwidth}
    from below:\\[.5ex]
    {\small
    \begin{tabular}{|l|l|}
      \hline
      $x$ & $f(x)$ \\
      \hline
      $0.5$ & $0.66667$ \\
      \hline
      $0.9$ & $0.52632$ \\
      \hline
      $0.99$ & $0.50251$ \\
      \hline
      $0.999$ & $0.50025$ \\
      \hline
    \end{tabular}
    }
    \end{minipage}\pause~~~
    \begin{minipage}{.49\textwidth}
    from above:\\[.5ex]
    {\small
    \begin{tabular}{|l|l|}
      \hline
      $x$ & $f(x)$ \\
      \hline
      $1.5$ & $0.40000$ \\
      \hline
      $1.1$ & $0.47619$ \\
      \hline
      $1.01$ & $0.49751$ \\
      \hline
      $1.001$ & $0.49975$ \\
      \hline
    \end{tabular}
    }
    \end{minipage}
  \end{minipage}
  \pause
  
  \begin{exampleblock}{}
    From these values we guess that $\lim_{x\to 1} \frac{x-1}{x^2-1} = 0.5$.
  \end{exampleblock}
\end{frame}