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\begin{frame}
  \frametitle{Precise Definition of Limits}

  \precisebook
  \bigskip
  \pause
  
  \emph{Geometric interpretation:}
  \medskip
  
  \mpause[1]{
  For any \textcolor{cred}{small interval $(L-\epsilon,L+\epsilon)$ around $L$},
  }\\
  \mpause[2]{
  we can find \textcolor{cgreen}{an interval $(a-\delta,a+\delta)$ around $a$}
  }\\
  \mpause[3]{
  such that $f$ maps all points in \textcolor{cgreen}{$(a-\delta,a+\delta)$} 
  into \textcolor{cred}{$(L-\epsilon,L+\epsilon)$}.
  }
  \bigskip  
  \begin{center}
    \begin{tikzpicture}[default]
      \draw[->] (0,0) -- ++(5cm,0);
      \draw[->] (6cm,0) -- ++(5cm,0);
      \begin{scope}[cgreen,ultra thick]
        \node[include] at (2.5,0) {};
        \node[anchor=north] at(2.5,-.1) {$a$};
      \mpause[2]{
        \draw[(-)] (1,0) -- 
            node[at start,below,yshift=-1mm] {$a-\delta$} 
            node[at end,below,yshift=-1mm] {$a+\delta$} 
          ++(3,0);
      }
      \end{scope}
      \begin{scope}[cred,ultra thick,xshift=6cm]
        \node[include] at (2.5,0) {};
        \node[anchor=north] at(2.5,-.1) {$L$};
      \mpause[1]{
        \draw[(-)] (1,0) -- 
            node[at start,below,yshift=-1mm] {$L-\epsilon$} 
            node[at end,below,yshift=-1mm] {$L+\epsilon$} 
          ++(3,0);
      }
      \end{scope}
      \draw[cblue,->,ultra thick,shorten >= 1mm] (1.5,0) to[out=90,in=110,looseness=.3] node[at start,above,yshift=2mm] {$x$} node[at end,above,yshift=3mm] {$f(x)$} (9.5,0);
    \end{tikzpicture}
  \end{center}
  \vspace{10cm}
\end{frame}