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

  \begin{exampleblock}{}
    For exponential function we have:
    \begin{talign}
      \lim_{x \to \infty} a^x &= 0 &&\text{for $0 \le a < 1$}\\[1ex]
      \lim_{x \to -\infty} a^x &= 0 &&\text{for $a > 1$}
    \end{talign}
  \end{exampleblock}
  \pause\bigskip
  
  \begin{exampleblock}{}
    For any polynomial $P$ and $a > 1$ we have
    \begin{talign}
      \lim_{x \to \infty} \frac{P(x)}{a^x} &= 0
    \end{talign}
    since the exponential function grows after than any polynomial.
  \end{exampleblock}
  \pause\bigskip
  
  \begin{exampleblock}{}
    For any polynomial $P$ and \alert{$0 < a < 1$} we have
    \begin{talign}
      \lim_{x \to \alert{-}\infty} \frac{P(x)}{a^x} &= 0
    \end{talign}
  \end{exampleblock}
\end{frame}