\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}