\begin{frame} \frametitle{Infinite Limits: Example} Consider the following graph of function $g(x)$: \begin{center} \scalebox{.6}{ \begin{tikzpicture}[default] \diagram{-4}{9}{-1.5}{3.2}{1} \diagramannotatez \diagramannotatex{-4,-3,-2,-1,1,2,3,4} \diagramannotatey{-1,1,2,3} \draw[cred] plot[smooth,domain=-4:-2,samples=30] function{2*sqrt((x+4)/2)}; \draw[cred] plot[smooth,domain=-2:0,samples=20] function{4/(x+4)}; \draw[cred] (0,-1) to[out=51,in=180] (3,3); \draw[cred] plot[smooth,domain=3:5,samples=1000] function{2-sin(5*pi/(x-5))}; \draw[cred] plot[smooth,domain=5:9,samples=20] function{3-((x-7)**2)/4}; \node[exclude={cred}] at (-2,2) {}; \node[include={cred}] at (0,1) {}; \node[exclude={cred}] at (0,-1) {}; \node[exclude={cred}] at (1,1) {}; \end{tikzpicture} } \end{center} Use the graph to estimate the following values: \smallskip \begin{minipage}{.39\textwidth} \begin{itemize} \item $\lim_{x\to 3^-} g(x) = \pause 3$\pause \item $\lim_{x\to 3^+} g(x) = \pause 3$\pause \item $\lim_{x\to 3} g(x) = \pause 3$\pause \item $\lim_{x\to 1} g(x) = \pause 1$\pause \item $g(1) = \pause \text{undefined}$\pause \item $g(0) = \pause 1$\pause \end{itemize} \end{minipage} \begin{minipage}{.59\textwidth} \begin{itemize} \item $\lim_{x\to 0^-} g(x) = \pause 1$\pause \item $\lim_{x\to 0^+} g(x) = \pause -1$\pause \item $\lim_{x\to 0} g(x) = \pause \text{does not exist}$\hspace*{-2cm}\pause \item $\lim_{x\to 5^-} g(x) = \pause \text{does not exist}$\hspace*{-2cm}\pause \item $\lim_{x\to 5^+} g(x) = \pause 2$\pause \item $\lim_{x\to 5} g(x) = \pause \text{does not exist}$\hspace*{-3cm}\hphantom{a} \end{itemize} \end{minipage} \vspace{10cm} \end{frame}