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.
-> Horizontal asymptote: Horizontal Asymptotes are the horizontal lines in which graph of function tend to a → + ∞.
The horizontal line is given by:
⇒a = c; the given equation is a Horizontal Asymptotes of a function a = f (t);
If it satisfy the given equation
⇒lim t → - ∞ f (t) = c
Or, we can write it as:
⇒lim t→ + ∞ f (t) = c.
Now we will see how to solve horizontal asymptotes? Take an example and see how to solve horizontal asymptote?
Let f (t) = (2t – 1) (t + 3)
t (t – 2)
As we know that the given function is in factor form, first we will convert the given function in the standard form. To find standard form we have to multiply the given values.
So, the standard form of the equation is:
From the given equation we neglect every value except the biggest exponents of ‘t’ which is present in numerator and denominator.
So we can write it as:
⇒f (t) = 2t2
On solving we get 2.
So the Horizontal Asymptote for the horizontal line y = 2.
-> Vertical asymptote: The equation of vertical line is given by:
⇒x = t;
Given equation is a vertical asymptotes of a graph which has a function y = f (t); this function is applicable when one of the given condition is true.
The two conditions are shown below:
1. lim t → a- f (t) = + ∞;
2. lim t → a+ f (t) = + ∞;
This is a brief introdution of horizontal asymptote definition and Vertical Asymptote.
In coordinate Geometry, an Asymptote of a curve is generally a straight line that approaches the curve so close that it tends to meet the curve at infinite Position, but it never intersects the line. There are two types of asymptotes which are:
. Vertical asymptotes
. Horizontal asymptotes
If graph of a function approaches as x –>±∞, for horizontal lines th...Read More