5.2. Function asymptotes

The line L is called the asymptote of the curve. , if the distance from a certain point of the curve M (x, y) to the straight line L tends to zero with an unlimited distance of this point along the curve from the origin (that is, if at least one of the coordinates of the point M tends to infinity).

Asymptotes are divided into vertical and oblique.

Straight called the vertical asymptote curve , if a and (or) .

Straight called the sloped asymptote curve if there are finite limits:
; . If it turns out that k = 0, then the asymptote is called horizontal.