\begin{frame} \frametitle{Calculating Limits using Limit Laws} \begin{alertblock}{} We have seen that calculating limits with a calculator sometimes leads to incorrect results. \end{alertblock} \pause\bigskip We will now see how to compute limits using \emph{Limit Laws}: \pause \begin{block}{} Let $c$ be a constant, and let $\lim_{x\to a} f(x)$ and $\lim_{x\to a} g(x)$ exist. Then \begin{enumerate} \pause \item $\lim_{x\to a} \;[f(x) + g(x)] = \lim_{x\to a} f(x) + \lim_{x\to a} g(x)$ % \\ \textcolor{gray}{(The limit of the sum is the sum of the limits)} \pause \item $\lim_{x\to a} \;[f(x) - g(x)] = \lim_{x\to a} f(x) - \lim_{x\to a} g(x)$ % \\ \textcolor{gray}{(The limit of the difference is the difference of the limits)} \pause \item $\lim_{x\to a} \;[c \cdot f(x)] = c \cdot \lim_{x\to a} f(x)$ \pause \item $\lim_{x\to a} \;[f(x) \cdot g(x)] = \lim_{x\to a} f(x) \cdot \lim_{x\to a} g(x)$ % \\ \textcolor{gray}{(The limit of a product is the product of the limits)} \pause \item $\lim_{x\to a} \frac{f(x)}{g(x)} = \frac{\lim_{x\to a} f(x)}{\lim_{x\to a} g(x)}$ if $\lim_{x\to a} g(x) \ne 0$ \end{enumerate} \end{block} \bigskip\pause These laws also work for one-sided limits $\lim_{x\to a^\pm}$. \end{frame}