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

  \begin{exampleblock}{}
    Guess the value of $\lim_{x\to 1} g(x)$ where 
    \begin{talign}
      g(x) = \begin{cases}
        \frac{x-1}{x^2-1} & \text{for $x \ne 1$}\\
        2 & \text{for $x = 1$}\\
      \end{cases}
    \end{talign}
  \end{exampleblock}
  \pause
  
  \begin{center}
    \scalebox{.6}{
    \begin{tikzpicture}[default]
      \diagram{-1}{5}{-1}{5}{1}
      \diagramannotate
      \draw[cblue,ultra thick] plot[smooth,domain=-.8:4.5,samples=20] function{(x-1)/(x**2-1)};
  
      \def\x{1}
      \def\y{{.5}}
      \node[exclude={cblue}] at (\x,\y) {};
      \node[include={cblue}] at (\x,2cm) {};
    \end{tikzpicture}
    }
  \end{center}
  \pause
  \vspace{-1ex}
    
  \begin{exampleblock}{}
    As on the previous slide $\lim_{x\to 1} g(x) = 0.5$.\\
    (recall that $g(1)$ does not matter for $\lim_{x\to 1} g(x)$).
  \end{exampleblock}
\end{frame}