# asymptote

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

$$\underset{d(P,O)\to \mathrm{\infty}}{lim}d(P,l)=0,$$ |

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 $y=\frac{\mathrm{sin}x}{x}$ the asymptote $y=0$.

Title | asymptote |
---|---|

Canonical name | Asymptote |

Date of creation | 2013-03-22 14:32:59 |

Last modified on | 2013-03-22 14:32:59 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 12 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 51N99 |

Related topic | SincFunction |

Related topic | FamousCurvesInThePlane |