\begin{frame} \frametitle{Limit: Examples} \begin{exampleblock}{} Guess the value of $\lim_{x\to 1} g(x)$ where \begin{talign} g(x) = \begin{cases} \frac{x-1}{x^2-1} & \text{for $x \ne 1$}\\ 2 & \text{for $x = 1$}\\ \end{cases} \end{talign} \end{exampleblock} \pause \begin{center} \scalebox{.6}{ \begin{tikzpicture}[default] \diagram{-1}{5}{-1}{5}{1} \diagramannotate \draw[cblue,ultra thick] plot[smooth,domain=-.8:4.5,samples=20] function{(x-1)/(x**2-1)}; \def\x{1} \def\y{{.5}} \node[exclude={cblue}] at (\x,\y) {}; \node[include={cblue}] at (\x,2cm) {}; \end{tikzpicture} } \end{center} \pause \vspace{-1ex} \begin{exampleblock}{} As on the previous slide $\lim_{x\to 1} g(x) = 0.5$.\\ (recall that $g(1)$ does not matter for $\lim_{x\to 1} g(x)$). \end{exampleblock} \end{frame}