An Asymptote is basically a line in which a graph approaches, but it never intersects the line. For example: In the following given graph of P =1 / Q, (here the x axis is denoted by ‘P’ and y axis is denoted by Q) the line approaches the p-axis (Q=0), but the line never touches it. The line can reach to infinity but it never touch. The line will not actually reach Q = 0, but will always get closer and closer.
It means the line Q = 0 is along to the Horizontal Asymptote. Horizontal asymptotes arise mostly when the given function is a fraction where the top part remains positive, but the bottom part goes to infinity. We will see in the example that the value Q = 1 / P is a fraction. If we find the infinity on the x-axis then the top of the fraction remains 1, but the bottom fraction gets bigger and bigger. As a result we can say that the entire fraction actually gets smaller, although it will not be zero. The function will be 1/2, then 1/3, then 1/10, even 1/10000, but never quite 0. Thus, Q = 0 is a horizontal asymptote for the function y = 1 / p. this is how to define asymptote.
Now we will see some types of asymptote which are mention below:
Vertical asymptote and Horizontal asymptote:
Let’s have a small introduction about Horizontal asymptotes.
Horizontal Asymptotes: Horizontal Asymptotes are the horizontal lines in which the graph of the function tends to x → + ∞.
The horizontal line is given by:
⇒u = c; the given equation is a Horizontal Asymptotes of a function u = f (p);
If it satisfy the given equation, and the equation is shown below.
⇒lim p → - ∞ f (p) = c or we can write it as:
⇒lim p → + ∞ f (p) = c.
This is the asymptote definition.
In coordinate Geometry, an Asymptote of a curve is basically a line which approaches the curve arbitrarily so close that it tends to meet the curve at infinite, but it never intersects the line. In classical mathematics it was said that an asymptote and the curve never meets but modernly such as in algebraic geometry, an asymptote of a curve is a line which is Tangent t...Read More
In Geometry, an Asymptote of a curve is a line in which the distance measured between the curve and the line approaches to zero but it tends to infinity. Let's see the different types of asymptote which are shown below:
There are two types of asymptotes one is Vertical Asymptote and another is Horizontal Asymptote. Now we will see asymptote formula. The asymptote for...Read More
Asymptote of a curve can be defined as a line in such a way that the distance between curve and line reaches to value zero as they tends to infinity. In coordinate Geometry generally there are two type of Asymptote.
In Asymptote the distance between the curve and line approaches to zero but it never intersect and tends to infinity.
Let’s see different types of asymptote which are shown below:
Horizontal asympt...Read More