\begin{frame} \frametitle{Infinite Limits: Example} Consider the following graph of function $g(x)$: \begin{center} \scalebox{.6}{ \begin{tikzpicture}[default] \diagram{-2}{5}{-4}{3}{1} \diagramannotatez \diagramannotatex{-1,1,2,3,4} \diagramannotatey{1} \draw[cred,ultra thick] plot[smooth,domain=-2:2,samples=20] function{2.2-.2*(x-1)**2}; \draw[cred,ultra thick] plot[smooth,domain=2.5:4.7,samples=20] function{-1/((x-2)**2)}; \node[exclude={cred}] at (2,2) {}; \node[include={cred}] at (2,1) {}; \end{tikzpicture} } \end{center} \vspace{-1ex} Use the graph to estimate the following values: \begin{itemize} \pause \item $f(2) = \alt<-2>{?}{1}$ \only<-2>{\choice{a} $0$ \choice{b} $1$ \choice{c} $2$ \choice{d} undefined} \pause\pause \item $\lim_{x\to 2^-} = \alt<-4>{?}{2}$ \only<-4>{\choice{a} $1$ \choice{b} $2$ \choice{c} $\infty$ \choice{d} $-\infty$ \choice{e} does not exist\hspace*{-2cm}} \pause\pause \item $\lim_{x\to 2^+} = \alt<-6>{?}{-\infty \text{ (special case of `does not exist')}}$ \only<-6>{\choice{a} $1$ \choice{b} $2$ \choice{c} $\infty$ \choice{d} $-\infty$ \choice{e} does not exist\hspace*{-2cm}} \pause\pause \item $\lim_{x\to 2} \alt<-8>{= ?}{\text{ does not exist}}$ \only<-8>{\choice{a} $1$ \choice{b} $\infty$ \choice{c} $-\infty$ \choice{d} does not exist\hspace*{-3cm}} \end{itemize} \pause \vspace{10cm} \end{frame}