\begin{frame} \frametitle{Computing Limits: Function Replacement} \begin{exampleblock}{} Find \begin{talign} \lim_{h\to 0} \frac{(3+h)^2 - 9}{h} \end{talign} \pause We have: \begin{talign} \frac{(3+h)^2 - 9}{h} \mpause[1]{ = \frac{9 + 6h + h^2 - 9}{h}} \mpause[2]{ = \frac{6h + h^2}{h}} \mpause[3]{ \stackrel{\text{\alert{for $h \ne 0$}}}{=} 6 + h } \end{talign} \pause\pause\pause\pause As a consequence: \begin{talign} \lim_{h\to 0} \frac{(3+h)^2 - 9}{h} = \lim_{h\to 0} (6+h) \mpause[1]{ = 6} \end{talign} \end{exampleblock} \end{frame}