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\begin{frame}
  \frametitle{Precise Definition of Limits}
  
  \precise
  \pause\bigskip
  
  In words: No matter what $\epsilon > 0$ we choose,
  \begin{itemize}
    \item[] if the distance of $x$ to $a$ is smaller than $\delta(\epsilon)$ (and $x\ne a$)
    \item[] then the distance of $f(x)$ to $L$ is smaller than $\epsilon$.
  \end{itemize}
  \pause\bigskip

  We can make $f$ \alert{arbitrarily close} to $L$ by taking $\epsilon$ arbitrarily small.
  \pause\\[1ex]
  
  Then $x$ is \alert{sufficiently close} to $a$ if the distance is $< \delta(\epsilon)$.
  \vspace{10cm}
\end{frame}