Question

How do you find vertical, horizontal and oblique asymptotes for `(x^2-16)/(x^4)`?

Answer 1

The vertical asymptote is `x=0`
The horizontal asymptote is `y=0`

Explanation:

As you cannot divide by 0, so `x=0` is a vertical asymptote

The degree of the numerator is `>` degree of the denominator, there is no oblique asymptote.

Limit`x^2/x^4=1/x^2=0^+`
`x->+-oo`

So `y=0` is a horizontal asymptote

graph{(x^2-16)/x^4 [-6.93, 8.874, -5.09, 2.81]}