\documentclass[14pt]{beamer}
\usetheme{Warsaw}
\usepackage{ulem, lscape, url, xcolor, outlines, csquotes}

\title[What Is Continuity]{What Kinds of Discontinuities Are There?}
\author{Mr. Sorice}
\date{A.P. Calculus AB/Calculus I \\ Lesson II.iii.2 \\ \today}

\begin{document}

\begin{frame} %1
    \titlepage
\end{frame}

\begin{frame} %2
    \frametitle{Recall: Formal Definition of Continuity}
    \begin{displayquote}
         Let $f$ be a function and $c$ a value of its domain.
         Then $f$ is continuous at $c$ if and only if:
         $$\lim_{x \to c} f(x) = f(c).$$
         \pause
     \end{displayquote}
     Remember: continuity \emph{works both ways} and is \emph{all or nothing}!
\end{frame}

\begin{frame} %3
    \frametitle{Over the limit}
    Let's return to the function I asked you to think about at the start of class.
    \begin{outline}
        \1 What's its limit as $x \to 0$?
        \pause
            \2 It has none!
        \pause
        \1 What ``went wrong" with its limit?
        \pause
        \1 How can we deal with it?
        \pause
            \2 What about \emph{handed limits}?
        \pause
        \1 Is it continuous at $x=0$?
        \pause
        \1 What ``went wrong" with its continuity?
    \end{outline}
\end{frame}

\begin{frame} %4
    \frametitle{What to do about it}
    Let's revisit our driving question:
    \pause \begin{displayquote}
        Are all discontinuous functions alike?
    \end{displayquote}
    \pause
    We've just looked at how one discontinuous function is, but are the all like that? Let's look at some functions and find out!
\end{frame}

\begin{frame} %5
    \frametitle{Activity Time}
    Questions before we begin? \pause
    
    \begin{outline}
        \1 Get together with your home group.
            \2 Each group gets a worksheet and set of cards.
        \1 Remember our formal definition of \emph{continuity}, since it will help you to understand \emph{discontinuity}:
         \begin{displayquote} Given a function $f$ and a value $c$ in its domain, $f$ is continuous at $c$ if and only if $\displaystyle{\lim_{x \to c}} f(x) = f(c).$ \end{displayquote}         
         \1 Be prepared to share results with the class.
     \end{outline}
\end{frame}

\end{document}
