Question

find the horizontal asymptote of (f(x) = \frac{4x^6 + 5x}{-3x^5 + 4x^4 + 3x^3 - 4x}) if it has one (if it doesnt, enter dne)

(y = )

Explanation:

Step 1: Identify the degrees of the polynomials

The degree of the numerator is \(n = 6\) and the degree of the denominator is \(d = 5\).

Step 2: Compare the degrees

Since \(n > d\) (\(6 > 5\)), the function has no horizontal asymptote.

Step 3: State the final result

The horizontal asymptote does not exist, so we enter DNE.

Answer:

DNE