# How do you find vertical, horizontal and oblique asymptotes for #f(x) =(4x^5)/(x^3-1)#?

##### 1 Answer

Dec 6, 2016

Vertical+

#### Explanation:

By actual division

As

So, x = 1 is the asymptote.

I surmise that the origin is not point of inflexion, despite that

seemingly it is so.

The curve is flat there, upon the x-axis, in infinitesimal

neighborhood. In other words, y and all its derivatives are 0, And so,

thereabout the origin , there is no series expansion.

graph{y(x^3-1)-4x^5=0 [-40, 40, -20, 20]} }