Question

How do you find the asymptotes for `f(x)=x/(x^2+4)`?

Answer 1

`y=0` is a horizontal asymptote

Explanation:

Take the limit of `f(x)` as x approaches `oo`

`Lim_(x->oo) f(x)=Lim_(x->oo) x/(x^2+4)=Lim_(x->oo) 1/(x+4/x)=0`

As `x->oo` the function `y=f(x)->0`

then `y=0` is a horizontal asymptote.

God bless you.