\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}