PlanetMath: asymptote

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asymptote

(Definition)

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

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

where

means the distance of the point

of the branch from the origin and

the distance of

from the line

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 .

$\includegraphics{asympt1}$

"asymptote" is owned by pahio. [ full author list (2) ]

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See Also: sinc function, famous curves

This object's parent.

Attachments:: asymptotes of graph of rational function (Definition) by eshyvari
asymptote of Lamé's cubic (Example) by pahio

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Cross-references: curve, hyperbola, point, line, origin, plane curve
There are 13 references to this entry.

This is version 9 of asymptote, born on 2004-08-11, modified 2008-03-14.
Object id is 6100, canonical name is Asymptote.
Accessed 3854 times total.

Classification:

AMS MSC:

51N99 (Geometry :: Analytic and descriptive geometry :: Miscellaneous)

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