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\begin{frame}
  \frametitle{Limits at Infinity: Horizontal Asymptotes}

  \begin{block}{}
    The line $y = L$ is called \emph{horizontal asymptote}
    of a function $f$ if
    \begin{talign}
      \lim_{x\to\infty} f(x) = L &&\text{or} &&\lim_{x\to-\infty} f(x) = L 
    \end{talign}
  \end{block}
  \pause\bigskip
 
  \only<2>{
  \begin{exampleblock}{}
  The function $f(x) = \frac{x^2 - 1}{x^2 + 1}$ has a horizontal asymptote at $y = 1$.
  \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}  
  \end{exampleblock}
  }
  
  \only<3>{
  \begin{exampleblock}{}
  The inverse tangent $\tan^{-1}$ has horizontal asymptotes
  \begin{talign}
    y = -\frac{\pi}{2} && \text{and} && y = \frac{\pi}{2}
  \end{talign}
  \begin{center}
    \scalebox{.7}{
    \begin{tikzpicture}[default,yscale=.8]
      \diagram{-7}{7}{-2}{2}{1}
      \diagramannotatez
      \diagramannotatexx{-pi/$-\pi$,pi/$\pi$}
      \diagramannotateyy{{-0.5*pi}/$-\frac{\pi}{2}$,{0.5*pi}/$\frac{\pi}{2}$}
      \draw[cgreen,ultra thick] plot[smooth,domain=-7:7,samples=50] function{atan(x)};
      \onslide<2->{
        \draw[cred,dashed] (-7,-0.5*pi) -- (7,-0.5*pi);
        \draw[cred,dashed] (-7,0.5*pi) -- (7,0.5*pi);
      }
    \end{tikzpicture}
    }
  \end{center}\vspace{-1ex}
  \pause
  \begin{talign}
    \lim_{x\to -\infty} \tan^{-1}{x} = -\frac{\pi}{2} && \lim_{x\to \infty} \tan^{-1}{x} = \frac{\pi}{2}
  \end{talign}
  \end{exampleblock}
  }
  \vspace{10cm}
\end{frame}