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When the numerator of a rational function has degree exactly one greater than the denominator, the function has an oblique (slant) asymptote. The asymptote is the polynomial term after dividing the numerator and denominator. This phenomenon occurs because when dividing the fraction, there will be a linear term, and a remainder.
In physics and other fields of science, one frequently comes across problems of an asymptotic nature, such as damping, orbiting, stabilization of a perturbed motion, etc. Their solutions lend themselves to asymptotic analysis (perturbation theory), which is widely used in modern applied mathematics, mechanics and physics. But asymptotic methods ...
The section on Slant Asymptote is rather confusing. My math teachers are rather confused looking at it . Can someone who knows a little more about the slant asymptotes both check the math and make it a little easier to understand. --Omnipotence407 14:13, 16 January 2008 (UTC) Much confusion.--( fi ) 23:24, 4 March 2008 (UTC)
An asymptote is a straight line that a curve approaches but never meets or crosses. Informally, one may speak of the curve meeting the asymptote "at infinity" although this is not a precise definition. In the equation =, y becomes arbitrarily small in magnitude as x increases.
The folium of Descartes (green) with asymptote (blue) when = In geometry , the folium of Descartes (from Latin folium ' leaf '; named for René Descartes ) is an algebraic curve defined by the implicit equation x 3 + y 3 − 3 a x y = 0. {\displaystyle x^{3}+y^{3}-3axy=0.}
The asymptotic directions are the same as the asymptotes of the hyperbola of the Dupin indicatrix through a hyperbolic point, or the unique asymptote through a parabolic point. [1] An asymptotic direction is a direction along which the normal curvature is zero: take the plane spanned by the direction and the surface's normal at that point. The ...
These expressions have an asymptote x = 1 (for a ≠ 0). The point most distant from the asymptote is (1 + a, 0). (0,0) is a crunode for a < −1.
This article is a list of notable unsolved problems in astronomy. Problems may be theoretical or experimental. Theoretical problems result from inability of current theories to explain observed phenomena or experimental results. Experimental problems result from inability to test or investigate a proposed theory.