\begin{frame}
  \frametitle{Limit: Examples}

  \begin{exampleblock}{}
    Guess the value of 
    \begin{talign}
      \lim_{x\to 0} \sin \frac{\pi}{x}
    \end{talign}
  \end{exampleblock}
  \pause
  \smallskip
  
  \begin{center}
  \begin{minipage}{.29\textwidth}
  \scalebox{.9}{\small
  \begin{tabular}{|l|l|}
    \hline
    $x$ & $f(x)$ \\
    \hline
    $\pm 1$ & $0$ \\
    \hline
    $\pm 0.1$ & $0$ \\
    \hline
    $\pm 0.01$ & $0$ \\
    \hline
    $\pm 0.001$ & $0$ \\
    \hline
  \end{tabular}
  }
  \end{minipage}~~~
  \begin{minipage}{.59\textwidth}
    \pause
    This suggest that the limit is $0$.
    \bigskip
    \pause
    
    However, this is \alert{wrong}:
  \end{minipage}
  \end{center}

  \begin{center}
    \scalebox{.6}{
    \begin{tikzpicture}[default]
      \diagram{-6}{6}{-1}{1.5}{1}
      \diagramannotatez
      \diagramannotatex{-1,1}
      \diagramannotatey{1}
      \draw[cblue] plot[smooth,domain=-6:6,samples=2000] function{sin(pi/ x)};
  
      \def\x{0}
      \def\y{{1}}
      \node[exclude={cblue}] at (\x,\y) {};
    \end{tikzpicture}
    }
  \end{center}
  \vspace{-1ex}
  \pause
  
  \begin{exampleblock}{}
    $\sin(\frac{\pi}{x}) = 0$ for arbitrarily small $x$, but also\\
    \pause
    $\sin(\frac{\pi}{x}) = 1$ for arbitrarily small $x$; \pause e.g. $x = \frac{1}{2.5}$, \pause $\frac{1}{4.5}$, \pause $\frac{1}{6.5}$,\ldots\\[.5ex]
    \pause
    Hence: \alert{The limit $\lim_{x\to 0} \sin \frac{\pi}{x}$ does not exist.}
  \end{exampleblock}

  \vspace{10cm}
\end{frame}