\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}