Question

How do you find vertical, horizontal and oblique asymptotes for `x/(1-x)^2`?

Answer 1

`y=0`

`x=1`

Explanation:

The degree of the bottom is 2, and the degree of the top is 1. Therefore, there will be a horizontal asymptote at `y=0` since the function will tend towards 0 as x goes to `oo`. This also means there will be no oblique asymptote.

As far as vertical asymptotes, they will occur when the denominator is 0 and the numerator is non-zero. For this function, this will happen when `x=1` since this makes the bottom equal to 0 and the top equal to 1.

So our asymptotes are `y=0` and `x=1`