\begin{frame} \frametitle{Limits at Infinity} \begin{exampleblock}{} Find $\lim_{x\to \infty} \frac{1}{x}$ and $\lim_{x\to -\infty} \frac{1}{x}$. \pause\medskip As $x$ gets larger, $\frac{1}{x}$ gets closer to $0$.\\ \pause Thus $\lim_{x\to \infty} \frac{1}{x} = 0$. \pause\medskip As $x$ gets larger negative, $\frac{1}{x}$ gets closer to $0$.\\ \pause Thus $\lim_{x\to -\infty} \frac{1}{x} = 0$. \pause \begin{center}\vspace{-1ex} \scalebox{.7}{ \begin{tikzpicture}[default,yscale=.8] \diagram{-4}{4}{-3}{3}{1} \diagramannotatez \diagramannotatex{1,1} \diagramannotatey{1,1} \draw[cgreen,ultra thick] plot[smooth,domain=.33:4,samples=20] function{1/x}; \draw[cgreen,ultra thick] plot[smooth,domain=-4:-.33,samples=20] function{1/x}; \draw[cred,ultra thick,dashed] (-4,0) -- (4,0); \end{tikzpicture} } \end{center}\vspace{-1ex} The function has the horizontal asymptote $y = 0$. \end{exampleblock} \end{frame}