\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}