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

  \begin{exampleblock}{}
    \vspace{-1ex}
    \begin{talign}
      f(x) = \begin{cases}
        2x - 1 &\text{for $x \ne 3$}\\
        6 &\text{for $x = 3$}
      \end{cases}
    \end{talign}
    We have derived
    \begin{talign}
      |f(x) - 5| < 0.1 \quad\text{ whenever }\quad 0 < |x-3| < 0.05
    \end{talign}
    \pause
    In words this means:
    \begin{itemize}
      \item [] If $x$ is within a distance of $0.05$ from $3$ (and $x \ne 3$)
      \item [] then $f(x)$ is within a distance of $0.1$ from $5$.
    \end{itemize}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}