\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}