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Asymptote of a Function

Tool to find the equations of the asymptotes (horizontal, vertical, oblique) of a function. The asymptotes are lines that tend (similar to a tangent) to function towards infinity.

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Asymptote of a Function -

Tag(s) : Mathematics

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Asymptote of a Function

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Asymptotes of a Function Calculator







Tool to find the equations of the asymptotes (horizontal, vertical, oblique) of a function. The asymptotes are lines that tend (similar to a tangent) to function towards infinity.

Answers to Questions

How to find an horizontal asymptote?

A function \( f(x) \) has an horizontal asymptote \( y=a \) if $$ \lim\limits_{x \rightarrow +\infty} f(x)=a \mbox{ or } \lim\limits_{x \rightarrow -\infty} f(x)=a \mbox{ (or both)}$$

There can not be more than 2 horizontal asymptotes.

How to find a vertical asymptote?

A function \( f(x) \) has a vertical asymptote \( x = a \) if it admits an infinite limit in \( a \).

$$ \lim\limits_{x \rightarrow \pm a} f(x)=\pm \infty $$

Generally, the function is not defined in \( a \), it is necessary to analyze the domain of the functionhref to find potential asymptotes.

There may be an infinite number of vertical asymptotes.

How to find an oblique asymptote?

A function \( f(x) \) has an oblique asymptote \( g(x)=ax+b \) when

$$ \lim\limits_{x \rightarrow \pm \infty} \left( f(x)-g(x)= 0 \right) $$

Computation may be simplified by calculating this limit :

$$ \lim\limits_{x \rightarrow \pm \infty} \left( rac{f(x)}{g(x)} = 1 \right) $$

How to find a non-linear asymptote?

A function \( f(x) \) has a non-linear asymptote \( g(x) \) when

$$ \lim\limits_{x \rightarrow \pm \infty} \left( f(x)-g(x)= 0 \right) $$

The method is the same as the oblique asymptote calculation.

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