Explain the terms Asymptote
Ans
Asymptote
In analytic geometry, an asymptote (/ˈæsɪmptoʊt/)
of a curve is a line such that the distance between the curve and the
line approaches zero as they tend to infinity. Some sources include the
requirement that the curve may not cross the line infinitely often, but this is
unusual for modern authors. In some contexts, such as algebraic
geometry, an asymptote is defined as a line which is tangent to a
curve at infinity.
The word asymptote is derived from
the Greek ἀσύμπτωτος
(asumptotos) which means "not falling together," from ἀ priv. +
σύν "together" + πτωτ-ός "fallen. The term was introduced
by Apollonius of Perga in his work on conic sections, but in
contrast to its modern meaning, he used it to mean any line that does not
intersect the given curve.
There are potentially three kinds of
asymptotes: horizontal, vertical and oblique asymptotes.
For curves given by the graph of a function y = ƒ(x),
horizontal asymptotes are horizontal lines that the graph of the function
approaches as x tends to +∞ or −∞. Vertical
asymptotes are vertical lines near which the function grows without bound.
More generally, one
curve is a curvilinear asymptote of another (as opposed to
a linear asymptote) if the distance between the two curves tends to
zero as they tend to infinity, although usually the term asymptote by
itself is reserved for linear asymptotes.
No comments:
Post a Comment