Question

What is the horizontal asymptote of 2x/(x^2 - 1)^(1/2)?

a) 0
b) 1
c) 2
d) There is no horizontal asymptote

Answer 1

The horizontal asymptote of the function 2x/(x^2 - 1)^(1/2) is y = 0 because the degree of the numerator is less than the degree of the polynomial inside the square root in the denominator.

Step-by-step explanation:

The horizontal asymptote of the function 2x/(x^2 - 1)^(1/2) can be determined by analyzing the behavior of the function as x approaches infinity. As the degree of the polynomial in the numerator is less than the degree of the polynomial inside the square root in the denominator, the horizontal asymptote is y = 0. This can also be confirmed by dividing the numerator and the denominator by the highest power of x in the denominator; as x goes to infinity, the terms that do not involve x approach zero, leaving the horizontal asymptote at y = 0.