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Vertical Asymptote

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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:
Vertical asymptote,
Horizontal asymptote:
Let’s have a small introduction about both the asymptotes. First we will see the vertical asymptote. As we know that, equation of vertical line is given by:
⇒x = s;
The given equation is a vertical asymptotes of the graph which has a function y = f (s); this given function is applicable when one of the given condition is true.
The two conditions are shown below:
1. lim s → a- f (s) = + ∞;
2. lim s → a+ f (s) = + ∞;
At Point ‘a’ the given function f (s) may or may not be defined and at point x = s the value does not affect the asymptote.
Let’s see the example: let a function f (s) is given:
F (s) = 1 / s if the value of s > 0;
5 if the value of s ≤ 0
The given function has a limit of + ∞ as s → 0+, the function f (s) has the vertical asymptote s = 0, even the value of f (0) = 5. The graph of this function interests the vertical asymptote at point (0, 5).
Horizontal Asymptotes: Horizontal Asymptotes are the horizontal lines in which a graph of a function tends to s → + ∞.
The horizontal line is given by:
⇒s = c; the given equation is a Horizontal Asymptotes of a function s = 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.

Vertical Asymptote Rules

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In analytical Geometry, an Asymptote of a curve is a line in such a way that the distance between the curve and the line approaches to zero and the curve line tends to infinity.
In mathematics, there are two types of asymptote which are mention below:
Vertical asymptote,
Horizontal asymptote
Now we will see the Vertical Asymptote rules.
As we know that the equation of vertical line is given by:
⇒x = v;
The given equation is a vertical asymptotes of the graph which has a function y = f (v); this given function is applicable when one of the given condition is true.
The two conditions are mention below:
1. lim v → a- f (v) = + ∞;
2. lim v → a+ f (v) = + ∞;
At Point ‘a’ the given function f (v) may or may not be defined and at point x = v the value does not affect the value of asymptote.
Now we will see an example of vertical asymptote.
Assume a vertical Asymptote Equation:

This given fraction is a rational fraction. We cannot put zero in the denominator of fraction as it give result as infinity, so we have to put the denominator value equal to zero.
On putting the denominator value is equal to zero we get:
⇒u2 - 5u – 6 = 0;
We can also write it as:
⇒(u – 6) (u + 1) = 0;
On further solving we get:
So value of u is 6 or -1;
So value of u is not 6 or -1 because it is divided by zero.
Horizontal Asymptotes: Horizontal Asymptotes are the horizontal lines in which the graph of function tends to s → + ∞.
The horizontal line is given by:
⇒s = c; the given equation is a Horizontal Asymptotes of a function s = f (p);
If it satisfy the given equation:
⇒lim p → - ∞ f (p) = c or we can write it as:
⇒lim p → + ∞ f (p) = c.