adjective Mathematics.
of or pertaining to an asymptote.
(of a function) approaching a given value as an expression containing a variable tends to infinity.
(of two functions) so defined that their ratio approaches unity as the independent variable approaches a limit or infinity.
(of a formula) becoming increasingly exact as a variable approaches a limit, usually infinity.
coming into consideration as a variable approaches a limit, usually infinity: asymptotic property; asymptotic behavior.
Also, asymptotical.

1665–75; asymptote + -ic

asymptotically, adverb Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
asymptotic or asymptotical (ˌæsɪmˈtɒtɪk)
1.  of or referring to an asymptote
2.  (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
asymptotical or asymptotical
asymptotically or asymptotical

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Example sentences
While the curve may be asymptotic, you would always get a little closer to your
Improvement will happen but it will approach an asymptotic limit.
Of course, this is an asymptotic result, since no stationary observer can be
  located at the horizon.
Over longer ranges, asymptotic limits and dimensionality become important.
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