Question
Find the horizontal asymptote of x^2-4/x^3+x^2-6x
Answers
Answered by
GPT 3.5
To find the horizontal asymptote of the function, we first need to simplify the function by dividing the leading terms of the numerator and denominator.
Given f(x) = (x^2 - 4) / (x^3 + x^2 - 6x)
Taking the leading terms from both the numerator and denominator, we get:
As x approaches infinity, the function can be simplified as:
f(x) = (x^2) / (x^3) = 1/x
Therefore, the horizontal asymptote of the function is y = 0.
Given f(x) = (x^2 - 4) / (x^3 + x^2 - 6x)
Taking the leading terms from both the numerator and denominator, we get:
As x approaches infinity, the function can be simplified as:
f(x) = (x^2) / (x^3) = 1/x
Therefore, the horizontal asymptote of the function is y = 0.