\begin{frame} \frametitle{Slant Asymptotes} Asymptotes that are neither horizontal nor vertical: \begin{block}{} If \vspace{-2ex} \begin{talign} \lim_{x\to\infty} [f(x) - (mx+b)] = 0 \end{talign} or \vspace{-2ex} \begin{talign} \lim_{x\to-\infty} [f(x) - (mx+b)] = 0 \end{talign} the the line $y = mx+b$ is called \emph{slant asymptote}. \end{block} \begin{center} \scalebox{.6}{ \begin{tikzpicture}[default,baseline=1cm] \diagram{-3}{3}{-3}{3}{1} \diagramannotatez \draw[red,dashed] (-3,-3) -- (3,3); \begin{scope}[ultra thick] \draw[cgreen,ultra thick] plot[smooth,domain=-3:3,samples=200] function{x**3/(x**2+1)}; \end{scope} \end{tikzpicture} } \end{center} \pause Note that the distance between curve and line approaches $0$. \end{frame}