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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.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.


(ˌæsɪmˈtɒtɪk) or


1. (Mathematics) of or referring to an asymptote
2. (Mathematics) (of a function, series, formula, etc) approaching a given value or condition, as a variable or an expression containing a variable approaches a limit, usually infinity
ˌasympˈtotically adv
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014


(ˌæs ɪmˈtɒt ɪk)

also as`ymp•tot′i•cal,

1. of or pertaining to an asymptote.
2. (of a function) approaching a given value as an expression containing a variable tends to infinity.
3. coming into consideration as a variable approaches a limit, usu. infinity: asymptotic property.
as`ymp•tot′i•cal•ly, adv.
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Adj.1.asymptotic - relating to or of the nature of an asymptote; "an asymptotic function"
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References in periodicals archive ?
Using the asymptotic analysis of Dyson-Schwinger (or loop) equations, Guionnet deals with strongly interacting systems of large numbers in which the interaction overcomes entropy.
We further pursue the asymptotic analysis for the ergodic sum rate and derive the asymptotic expression for the ergodic sum rate of NOMA relaying network over Nakagami-m fading channels.
Asymptotic analysis of difference equations of the form (5) or its explicit version often appeared in literature in the last decades.
The asymptotic analysis [26, 27] of the integral form, appearing in (12) for [tau] [much greater than] 1, provides the expression of the survival amplitude over long times:
The more subtle asymptotic analysis performed in this paper shows that when a large (x, t) region of variable changes is analyzed, transition to a simpler model may be groundless even at small oscillation amplitudes.
In this section, different asymptotic analysis is performed according to the condition of [[sigma].sup.2.sub.e] because when [[sigma].sup.2.sub.e] = 0 (i.e., perfect channel estimation), [R.sub.t] = ([2.sup.2R] - 1)/[[rho].sub.t], whereas when [[sigma].sup.2.sub.e] [not equal to] 0, [R.sub.t] = ([2.sup.2R] - 1)(1 + [[rho].sub.t]-[[sigma].sup.2.sub.e])/[[rho].sub.t] [approximately equal to] ([2.sup.2R] - 1)[[sigma].sup.2.sub.e] by high SNR approximation.
Fang, "Asymptotic analysis of an axially viscoelastic string constituted by a fractional differentiation law," International Journal of Non-Linear Mechanics, vol.
They performed exact analysis of the outage probability as well as asymptotic analysis when the number of primary nodes goes to infinity.
This technical complication, conveniently managed, does not distort the asymptotic analysis of [F.sub.1](x).
As Markov sources are closely related to automata and transducers, our results can also be used for the asymptotic analysis of sequences which can be computed by transducers.
To carry out the desired asymptotic analysis, we need the following assumptions: