Question

How to find horizontal asymptotes of 2x/x²+1?

a) Set the numerator equal to zero and solve for x.
b) Compare the degrees of the numerator and denominator.
c) Take the limit as x approaches infinity or negative infinity.
d) Find the points of intersection with the x-axis.

Answer 1

To find the horizontal asymptotes of the function f(x) = 2x/(x²+1), one must compare the degrees of the numerator to the denominator and take the limit as x approaches infinity. The horizontal asymptote for this function is y = 0.

Step-by-step explanation:

The question is about finding horizontal asymptotes for the function f(x) = 2x/(x²+1). To find the horizontal asymptotes of the function f(x) = 2x/(x²+1), one must compare the degrees of the numerator to the denominator and take the limit as x approaches infinity. The horizontal asymptote for this function is y = 0.

To find the horizontal asymptotes, you should compare the degrees of the numerator and the denominator (Option b) and take the limit as x approaches infinity or negative infinity (Option c). In this case, the degree of the numerator (degree 1) is less than the degree of the denominator (degree 2), which means the horizontal asymptote is y = 0.

This is because as x approaches infinity or negative infinity, the value of x² grows much faster than the value of 2x, causing the fraction to approach zero.