Question

find the horizontal asymptote of ( f(x)=\frac{2 x^{7}-3 x}{-3 x^{5}+2 x^{2}-4 x} ). if the horizontal asymptote does not exist, enter dne. the horizontal asymptote is ( y= )

Explanation:

Step1: Determine the degrees of numerator and denominator

The degree of the numerator \(n\) (for \(2x^{7}-3x\)) is \(n = 7\). The degree of the denominator \(m\) (for \(-3x^{5}+2x^{2}-4x\)) is \(m = 5\).

Step2: Apply the rule for horizontal asymptotes

If \(n>m\), the horizontal asymptote does not exist. Since \(7 > 5\) (where \(n = 7\) and \(m = 5\)).

Answer:

DNE