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\begin{frame}
\frametitle{Continuity: Examples}

\begin{exampleblock}{}
Where is $\frac{x^2 - x -2}{x-2}$ (dis)continuous?
\begin{itemize}
\pause
\item discontinuous at $x = 2$ since $f(2)$ is undefined
\pause
\item continuous everywhere else by direct substitution property
\end{itemize}
\end{exampleblock}
\pause\bigskip

\begin{exampleblock}{}
Where is
\begin{talign}
f(x) = \begin{cases}
\frac{1}{x^2} &\text{for $x \ne 0$}\\
1 &\text{for $x = 0$}
\end{cases}
\end{talign}
(dis)continuous?
\begin{itemize}
\pause
\item discontinuous at $x = 0$ since $\lim_{x\to0} f(x)$ does not exist
\pause
\item continuous everywhere else by direct substitution property
\end{itemize}
\end{exampleblock}
\end{frame}