4/119
\begin{frame}
  \frametitle{Limits at Infinity}
  
  Lets investigate the behavior of the function
  \begin{talign}
    f(x) = \frac{x^2 - 1}{x^2 + 1}
  \end{talign}
  when $x$ becomes large:

  \begin{center}
    \scalebox{.7}{
    \begin{tikzpicture}[default]
      \diagram{-7}{7}{-1.2}{1.3}{1}
      \diagramannotatez
      \diagramannotatex{-1,1}
      \diagramannotatey{1}
      \draw[cgreen,ultra thick] plot[smooth,domain=-7:7,samples=20] function{(x**2 - 1)/(x**2 + 1)};
      \onslide<2->{
        \draw[cred,dashed] (-7,1) -- (7,1);
      }
    \end{tikzpicture}
    }
  \end{center}  
  \pause
  
  As $x$ grows larger, the values of $f(x)$ get closer and closer to $1$.\\
  \pause\medskip
  
  This is expressed by
  \begin{talign}
    \lim_{x\to\infty} \frac{x^2 - 1}{x^2 + 1} = 1
  \end{talign}
\end{frame}