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

  \precisebook
  \bigskip
  
  \emph{Alternative geometric interpretation:}
  \medskip
  
  \begin{minipage}{.49\textwidth}
    \scalebox{.9}{
    \begin{tikzpicture}[default]
      {\def\diaborderx{1cm}
      \diagram{-.5}{3}{-.5}{3}{1}}
      \diagramannotatez

      \onslide<2->{      
      \draw[fill=cred,opacity=.2,draw=none] (-.25,1) rectangle ++(3.5,1);
      \draw[cred] (-.25,1) -- node[at start,left] {$L-\epsilon$} ++(3.5,0);
      \draw[cred] (-.25,2) -- node[at start,left] {$L+\epsilon$} ++(3.5,0);
      }
      \draw[cred,dashed] (-.25,1.5) -- node[at start,left] {$L$} ++(3.5,0);

      \onslide<3->{      
      \draw[fill=cgreen,opacity=.2,draw=none] (1.4,-.25) rectangle ++(.7,3.5);
      \draw[cgreen] (1.4,-.25) -- node[at start,rotate=90,left] {$a-\delta$} ++(0,3.5);
      \draw[cgreen] (2.1,-.25) -- node[at start,rotate=90,left] {$a+\delta$} ++(0,3.5);
      }
      \draw[cgreen,dashed] (1.75,-.25) -- node[at start,below] {$a$} ++(0,3.5);

      \draw[cblue,ultra thick] (-.5,2.5) to[out=0,in=-105,looseness=2.2] (3,2);
    \end{tikzpicture}
    }
  \end{minipage}~
  \begin{minipage}{.49\textwidth}
    \pause
    For every \textcolor{cred}{interval $I_L$ around $L$},\\[1ex]%
    \pause%
    find \textcolor{cgreen}{interval $I_a$ around $a$}\\[1ex]%
    \pause%
    such that\\[1ex]%
    if we restrict the domain of $f$ to \textcolor{cgreen}{$I_a$},
    then the curve lies in \textcolor{cred}{$I_L$}.
  \end{minipage}
  \vspace{10cm}
\end{frame}