\begin{frame} \frametitle{One-Sided Limits: Example} Consider the following graph of function $g(x)$: \begin{center} \scalebox{.6}{ \begin{tikzpicture}[default] \diagram{-2}{5}{-1}{4}{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=2:4.7,samples=20] function{2-(x-3)**2}; \node[exclude={cred}] at (2,2) {}; \node[exclude={cred}] at (2,1) {}; \node[exclude={cred}] at (4,1) {}; \node[include={cred}] at (4,3) {}; \end{tikzpicture} } \end{center} \vspace{-1ex} Use the graph to estimate the following values: \begin{itemize} \pause \item $\lim_{x\to 2^-} = \alt<-2>{?}{2}$ \only<-2>{\choice{a} $0$ \choice{b} $1$ \choice{c} $2$ \choice{d} $3$ \choice{e} does not exist} \pause\pause \item $\lim_{x\to 2^+} = \alt<-4>{?}{1}$ \only<-4>{\choice{a} $0$ \choice{b} $1$ \choice{c} $2$ \choice{d} $3$ \choice{e} does not exist} \pause\pause \item $\lim_{x\to 2} \alt<-6>{= ?}{\text{ does not exist}}$ \only<-6>{\choice{a} $0$ \choice{b} $1$ \choice{c} $2$ \choice{d} $3$ \choice{e} does not exist} \pause\pause \item $\lim_{x\to 4^-} = \alt<-8>{?}{1}$ \only<-8>{\choice{a} $0$ \choice{b} $1$ \choice{c} $2$ \choice{d} $3$ \choice{e} does not exist} \pause\pause \item $\lim_{x\to 4^+} = \alt<-10>{?}{1}$ \only<-10>{\choice{a} $0$ \choice{b} $1$ \choice{c} $2$ \choice{d} $3$ \choice{e} does not exist} \pause\pause \item $\lim_{x\to 4} = \alt<-12>{?}{1}$ \only<-12>{\choice{a} $0$ \choice{b} $1$ \choice{c} $2$ \choice{d} $3$ \choice{e} does not exist} \end{itemize} \pause \vspace{10cm} \end{frame}