An asymptote of a curve is a line that approaches zero when one or both of the x and y coordinates approaches infinity in analytic geometry. An asymptote of a curve is a line that is tangent to the curve at infinity, as defined in projective geometry and related settings.

Horizontal, vertical, and oblique asymptotes are the three types. Horizontal asymptotes are horizontal lines that the graph of a function approaches when x goes to +∞ or -∞ for curves defined by the graph of a function y = 𝑓(x). Vertical asymptotes are vertical lines when the function becomes unbounded. The slope of an oblique asymptote is non-zero but finite, and the graph of the function approaches it as x increases to +∞ or -∞.

A curvilinear asymptote of another curve (as opposed to a linear asymptote) occurs when the distance between the two curves approaches zero as they approach infinity, while the name asymptote is normally reserved for linear asymptotes. The asymptotes of a function are a crucial step in drawing its graph because they communicate information about the behavior of curves in the large. Asymptotes of functions, in a wide sense, are studied as part of the topic of asymptotic analysis.

Concepts of Asymptotes - Mathematics I

In this “Concepts of Asymptotes - Mathematics I” you will learn about the following topics:

  1. Introduction to Asymptotes
  2. Determination of asymptotes of algebraic curves
  3. Vertical asymptotes
  4. Horizontal asymptotes
  5. Oblique asymptotes
  6. Asymptotes of Algebraic curves
  7. Asymptotes of the curve in polar coordinates

==== Point to Note ====

This article Asymptotes - Mathematics I is contributed by Namrata Chaudhary, a student of Lumbini Engineering College (LEC).

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