Question

What are the oblique asymptote of `P(x)= 4x^5/(x^3-1)`?

Answer 1

The function has no oblique (linear) asymptotes.

Explanation:

When we do the division, we get:

`P(x)= (4x^5)/(x^3-1) = 4x^2+(4x^2)/(x^3-1)`

Although `P(x)` does get arbitrarily close to the parabola `y=4x^2`, a parabola is not an oblique asymptote.