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

  \begin{exampleblock}{}
    \begin{talign}
      \lim_{x \to \infty} \frac{f(x)}{g(x)} 
    \end{talign}
    A good \alert{heuristic (this is not a law)}  for to look at:
    \begin{itemize}
      \item the fastest growing addend of $f(x)$
      \item the fastest growing addend of $g(x)$
    \end{itemize}
    Typically, the other addends do not matter.
  \end{exampleblock}
  \pause
  
  \begin{exampleblock}{}
    \begin{malign}
      \lim_{x\to \infty} \frac{\alert<3->{3x^2} -x - 2}{\alert<3->{5x^2} + 4x + 1} = \mpause[2]{\frac{3}{5}}
    \end{malign}
  \end{exampleblock}
  \pause\pause\pause

  \begin{exampleblock}{}
    \begin{malign}
      \lim_{x\to \infty} \frac{\sqrt{5x^3+1} + \alert<6->{2x^2}}{\alert<6->{x^2} + 1} = \mpause[2]{2}
    \end{malign}
  \end{exampleblock}
  \pause\pause\pause

  \begin{exampleblock}{}
    \begin{malign}
      \lim_{x\to \infty} \frac{\alert<9->{5x^3} + x + \alert<9->{x\cdot x^2}}{\alert<9->{2x^3} - x} = \mpause[2]{3}
    \end{malign}
  \end{exampleblock}
\end{frame}