\begin{frame}
  \frametitle{Continuity}
  
  \begin{block}{}
    A function $f$ is \emph{continuous} at a number $a$ if
    \begin{talign}
      \lim_{x\to a} f(x) = f(a)
    \end{talign}
  \end{block}
  \pause\medskip
  The definition implicitly requires that:
  \begin{itemize}
  \pause
    \item $f(a)$ is defined
  \pause
    \item $\lim_{x\to a} f(x)$ exists
  \end{itemize}
  \pause\medskip
  Intuitive meaning of continuous:
  \begin{itemize}
  \pause
    \item gradual process without interruption or abrupt change 
  \pause
    \item small changes in $x$ produce only small change in $f(x)$
  \pause
    \item graph of the function can be drawn without lifting the pen 
  \end{itemize}
  \pause\medskip
  
  \begin{block}{}
    A function $f$ is \emph{discontinuous} at a number $a$ if
    \begin{itemize}
      \item $f$ is defined near $a$ (except perhaps a), and
      \item $f$ is not continuous at $a$
    \end{itemize}
  \end{block}
\end{frame}