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The x-axis and y-axis are asymptotes of the hyperbola xy = 3.


 (ăs′ĭm-tōt′, -ĭmp-)
A line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve.

[Ultimately from Greek asumptōtos, not intersecting : a-, not; see a-1 + sumptōtos, intersecting (from sumpiptein, sumptō-, to converge : sun-, syn- + piptein, to fall; see pet- in Indo-European roots).]

as′ymp·tot′ic (-tŏt′ĭk), as′ymp·tot′i·cal adj.
as′ymp·tot′i·cal·ly adv.
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Adv.1.asymptotically - toward an asymptote; "it grew asymptotically"
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References in periodicals archive ?
If we then design line control for this extended system such that will make it asymptotically stable with prescribed dynamics according to the reference model, this will automatically fulfil the desired control goal in steady state, as well as in very good quality in transient states.
The consumption of bait increased asymptotically and attained peak on the 7th night.
Higher-dimensional gravity and the gauge/gravity duality provide a strong motivation to investigate BHs in contexts formerly regarded as removed from physical applications, in particular asymptotically anti-de Sitter (AdS) spacetimes of more than four dimensions.
The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions.
In the paper [4], Byungchan Kim, Eunmi Kim and Jeehyeon Seo, by using the circle method of Wright [5] and some results from [2], proved the conjecture of Andrews-Chan-Kim-Osburn is asymptotically true.
The first static solution to the field equations of general relativity was found that same year describing the gravitational influence of an idealised, infinite density point mass on asymptotically flat space [4].
In order to show that the zero solution is globally asymptotically stable, we will have to require an additional condition.
This first of two volumes of proceedings contains 19 technical papers on such topics as instabilities in kinetic theory and their relationship to the ergodic theorem, the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes, an initial-boundary value problem in a strip for two-dimensional equations of Zacharov-Kunzhetsov type, an extension of harmonicity and holomorphy, and over-determined transforms in integral geometry.
2] being asymptotically stable, while there is stable focus in the plane, which is perpendicular to this direction.
Moreover, an EH always exists in black hole asymptotically flat space-time under a weak cosmic censorship condition and is represented by a Killing horizon such that the space-time is analytic and the stress tensor obeys the weak energy condition.
Then the system is uniformly asymptotically stable at equilibrium point x = 0.