\begin{frame}
  \frametitle{Computing Limits: Function Replacement}
  
  \begin{exampleblock}{}
    Find $\lim_{x\to 1} g(x)$ where
    \begin{talign}
      g(x) = \begin{cases}
        2x + 1 &\text{for $x\ne 1$},\\
        \pi &\text{for $x = 1$}
      \end{cases}
    \end{talign}
    \pause
    We have:
    \begin{talign}
      g(x) = 2x+1 \quad\text{for all $x\ne 1$}
    \end{talign}
    \pause
    As a consequence:
    \begin{talign}
      \lim_{x\to 1} g(x) = \lim_{x\to 1} 2x+1 \mpause[1]{ = 2 + 1 = 3}
    \end{talign}
  \end{exampleblock}
\end{frame}