Basic Concept on Asymptotes in Calculus

Abstract

In analytical geometry an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tend to infinity. Some source includes the requirements that the curve may not cross the line infinitely often but this is unusual for modern definition. In some content such as algebraic geometry an asymptote is defined as a line which is tangent to a curve at infinity.

In some case a curve may have a branch or branches extending beyond the finite region. In this case of p be a point on such a branch of the curve, having its coordinates (x,y) and if P moves along the curve, so that at least one of x and y tend to + ∞ and to -∞, then P is said to tend to infinites and this we denote by P → ∞