\begin{frame} \frametitle{Limits and One-Sided Limits} We recall the following theorem: \begin{block}{} \begin{malign} \lim_{x\to a} f(x) = L \quad \text{ if and only if } \quad \lim_{x\to a^-} f(x) = L = \lim_{x\to a^+} f(x) \end{malign} \end{block} \pause\bigskip The theorem in words: \begin{itemize} \item The limit of $f(x)$, for $x$ approaching $a$, is $L$ if and only if \\the left-limit and the right-limit at $a$ are both $L$. \end{itemize} \pause\bigskip The limit laws also apply for one-sided limits! \begin{itemize} % \pause % \item often easier to compute the one-sided limits \pause \item if $\lim_{x\to a^-} f(x) \alert{\ne} \lim_{x\to a^+} f(x)$\\ then $\lim_{x\to a} f(x)$ does not exist \end{itemize} \end{frame}