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

  \begin{exampleblock}{}
    Evaluate 
    \begin{talign}
      \lim_{x\to \infty} \sin(x) = \mpause[1]{\text{does not exist}}
    \end{talign}
    \pause\pause
    since $\sin(x)$ oscillates between $-1$ and $1$.
  \end{exampleblock}
  \pause
  
  \begin{exampleblock}{}
    Evaluate 
    \begin{talign}
      \lim_{x\to \infty} \frac{3\sin(x)}{x^2} = \mpause[1]{0}
    \end{talign}
    \pause\pause
    since the denominator grows to infinity while $-3 \le 3\sin(x) \le 3$.
  \end{exampleblock}
  \pause
  
  \begin{exampleblock}{}
    Evaluate 
    \begin{talign}
      \lim_{x\to \infty} \frac{2 x^3 + x^2 \cdot \cos(x) + 3e^x + x}{x^5 + 5e^x} = 
      \mpause[1]{\frac{3}{5}}
    \end{talign}
    \pause\pause
    since the exponential functions grow much faster than the rest.\\
    \pause
    To use limit laws, multiply numerator and denominator by $\frac{1}{e^x}$.
  \end{exampleblock}
  \pause\pause
\end{frame}