\begin{frame} \frametitle{Limits at Infinity} \begin{exampleblock}{} Evaluate \begin{talign} \lim_{x\to \infty} \frac{3x^5 + x^2 -2}{x^2 - x + 2^{x}} = \mpause[1]{0} \end{talign} \pause\pause since $2^x$ grows faster than any polynomial. \end{exampleblock} \pause \begin{exampleblock}{} Evaluate \begin{talign} \lim_{x\to \infty} \frac{3x^2 + x}{5x^2 - x + 5^{-x}} = \mpause[1]{\frac{3}{5}} \end{talign} \pause\pause since $\lim_{x\to \infty} 5^{-x} = 0$. \end{exampleblock} \pause \begin{exampleblock}{} Evaluate \begin{talign} \lim_{x\to 0^-} e^{\frac{1}{x}} = \mpause[1]{ \lim_{x\to -\infty} e^{x} = } \mpause[2]{ 0} \end{talign} \end{exampleblock} \pause\pause \end{frame}