\begin{frame} \frametitle{Infinite Limits at Infinity} \begin{block}{}\vspace{-2ex} \begin{talign} \lim_{x\to \infty} f(x) = \infty \end{talign} if we can make the values of $f(x)$ arbitrary large by taking $x$ sufficiently large. \end{block} \pause\medskip Similar for: \begin{talign} \lim_{x\to \infty} f(x) = -\infty && \lim_{x\to -\infty} f(x) = \infty && \lim_{x\to -\infty} f(x) = -\infty \end{talign} \pause \begin{exampleblock}{} \begin{malign} \lim_{x\to \infty} x^3 = \mpause[1]{\infty} && \mpause[2]{\lim_{x\to -\infty} x^3 = \mpause[3]{-\infty}} \end{malign} \end{exampleblock} \pause\pause\pause\pause \begin{exampleblock}{} \begin{malign} \lim_{x\to \infty} a^x &= \infty && \text{for \mpause[1]{$a > 1$} }\\ \mpause[2]{\lim_{x\to -\infty} a^x} &\mpause[2]{= \infty} && \mpause[2]{\text{for \mpause[3]{$0 < a < 1$}} } \end{malign} \end{exampleblock} \end{frame}