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

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Answer 1 · 2015-09-09T16:10:30

The function has no oblique (linear) asymptotes.

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.

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