Horizontal Asymptote Calculator

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Horizontal asymptote is the straight horizontal line drawn to a curve going towards infinity. As the curve goes towards infinity, the distance between the asymptote and the curve approaches ‘0’, but the asymptote never touches or crosses the curve. Horizontal asymptote calculator is the online tool which can give the equation of the horizontal asymptote to a given function.


Example 1:Find the horizontal asymptote to the function, y = (2x2 + 10)/ (x2 – 2x)

Given function: y = (2x2 + 10)/ (x2– 2x)

In order to find the horizontal asymptote to the given function, we should check the highest exponent of the variable in the numerator and in the denominator.

Highest exponent of ‘x’ in the numerator = Highest exponent of ‘x’ in the denominator

Hence > Divide the leading terms, 2x2 and x2 by ‘x2’ = 2/1 = 2

Horizontal asymptote > y = 2
 

Example 2: Find the horizontal asymptote to the function, y = (x + 3)/ (x2 – 2)

In order to find the horizontal asymptote to the given function, we should check the highest exponent of the variable in the numerator and in the denominator.

èHighest exponent of ‘x’ in the numerator < Highest exponent of ‘x’ in the denominator.

In this case, the function or the curve towards infinity will get closer and closer to the X-axis.

Hence in this case, always the horizontal asymptote is  y = 0



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