\begin{frame}
  \frametitle{Infinite Limits at Infinity}

  \begin{exampleblock}{}
    Evaluate
    \begin{talign}
      \lim_{x\to\infty} \frac{x^2 + x}{3-x}
    \end{talign}
    \pause
    We have
    \begin{talign}
      \lim_{x\to\infty} \frac{x^2 + x}{3-x}
      &\mpause[1]{ = \lim_{x\to\infty} \left( \frac{x^2 + x}{3-x} \cdot \frac{\frac{1}{x}}{\frac{1}{x}} \right) } \\
      &\mpause[2]{ = \lim_{x\to\infty} \frac{x + 1}{\frac{3}{x}-1} } \\
      &\mpause[3]{{\color{gray} = \frac{\infty}{0-1} }} \\
      &\mpause[4]{ = -\infty }
    \end{talign}
    \pause\pause\pause\pause\pause
    because $x + 1$ grows to infinity while $\frac{3}{x}-1$ gets closer to $-1$.
  \end{exampleblock}
\end{frame}