# asymptote

If a plane curve $\gamma$ has a continuing infinitely far from the origin $O$, then $\gamma$ may have an :  The direct line $l$ is an asymptote of $\gamma$, if

 $\lim_{d(P,\,O)\to\infty}d(P,\,l)=0,$

where $d(P,\,O)$ means the of the point $P$ of the from the origin and $d(P,\,l)$ the of $P$ from the line $l$.

Examples:  The hyperbola$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$  has the asymptotes  $y=\pm\frac{b}{a}x$;  the curve   $y=\frac{\sin x}{x}$  the asymptote  $y=0$.

Title asymptote Asymptote 2013-03-22 14:32:59 2013-03-22 14:32:59 pahio (2872) pahio (2872) 12 pahio (2872) Definition msc 51N99 SincFunction FamousCurvesInThePlane