What are the asymptote(s) and hole(s), if any, of # f(x) =x/(x^3-x)#?
Horizontal Asymptotes 0
An vertical asymptote or a hole is created by a point in which the domain is equal to zero i.e.
An horizontal asymptote is created where the top and the bottom of the fraction don't cancel out. Whilst a hole is when you can cancel out.
So as the
For horizontal asymptotes one is trying to find what happens as x approaches infinity or negative infinity and whether it tends to a particular y value.
To do this divide both the numerator and denominator of the fraction by the highest power of
To do this we have to know two rules
For limits to negative infinty we have to make all the
So the horizontal asymptote as x approaches