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##### Asked by: Goizane Strzyzesk

science space and astronomy# How do horizontal Asymptotes relate to limits at infinity?

Last Updated: 31st March, 2020

**limit at infinity**or negative

**infinity**is the same as finding the location of the

**horizontal asymptote**. there's no

**horizontal asymptote**and the

**limit**of the function as x approaches

**infinity**(or negative

**infinity**)

**does**not exist.

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Correspondingly, how do you find the horizontal asymptote of a limit?

**Horizontal Asymptotes** A function f(x) will have the **horizontal asymptote** y=L if either limx→∞f(x)=L or limx→−∞f(x)=L. Therefore, to find **horizontal asymptotes**, we simply evaluate the **limit** of the function as it approaches infinity, and again as it approaches negative infinity.

Secondly, what are the rules for horizontal asymptotes? **The three rules that horizontal asymptotes follow are based on the degree of the numerator, n, and the degree of the denominator, m.**

- If n < m, the horizontal asymptote is y = 0.
- If n = m, the horizontal asymptote is y = a/b.
- If n > m, there is no horizontal asymptote.

Likewise, people ask, how do Asymptotes relate to limits?

1 Answer. **Asymptotes are** defined using **limits**. A line x=a is called a vertical **asymptote** of a function f(x) if at least one of the following **limits** hold. A line y=b is called a horizontal **asymptote** of f(x) if at least one of the following **limits** holds.

Is an asymptote a limit?

A one-sided **limit** is a **limit** in which x is approaching a number only from the right or only from the left. An **asymptote** is a line that a graph approaches but does not touch. An **asymptote** that is a vertical line is called a vertical **asymptote**, and an **asymptote** that is a horizontal line is called a horizontal **asymptote**.