60/154
\begin{frame}
  \frametitle{Limit: Examples}

  \begin{exampleblock}{}
    Guess the value of 
    \begin{talign}
      \lim_{x\to 0} \left(x^3 + \frac{\cos 5x}{10000} \right)
    \end{talign}
  \end{exampleblock}
  \pause
  \smallskip
  
  \begin{center}
  \begin{minipage}{.39\textwidth}
    \scalebox{.7}{
    \begin{tikzpicture}[default]
      \diagram{-1.2}{1.3}{-1.2}{1.3}{1}
      \diagramannotatez
      \diagramannotatex{-1,1}
      \diagramannotatey{1}
      \draw[cblue,ultra thick] plot[smooth,domain=-1:1,samples=20] function{x**3 + cos(5*x)/10000};
    \end{tikzpicture}
    }
  \end{minipage}
  \pause
  \begin{minipage}{.39\textwidth}
  \scalebox{.9}{\small
  \begin{tabular}{|l|l|}
    \hline
    $x$ & $f(x)$ \\
    \hline
    $1$ & $1.000028$ \\
    \hline
    $0.5$ & $0.124920$ \\
    \hline
    $0.1$ & $0.001088$ \\
    \hline
    $0.01$ & $0.000101$ \\
    \hline
  \end{tabular}
  }
  \end{minipage}
  \end{center}
  \pause\medskip
  
  Looks like the limit is $0$. \pause But if we continue:

  \begin{center}
  \scalebox{.9}{\small
  \begin{tabular}{|l|l|}
    \hline
    $x$ & $f(x)$ \\
    \hline
    $0.005$ & $0.00010009$ \\
    \hline
    $0.001$ & $0.00010000$ \\
    \hline
  \end{tabular}
  }
  \end{center}
  \pause\medskip
  
  We see actually that:
  \begin{exampleblock}{}
    The value of the limit is $0.0001$.
  \end{exampleblock}

  \vspace{10cm}
\end{frame}