Question

What is the limit of `(x^2-4)/(2x-4x^2)` as x goes to infinity?

Answer 1

It is

`lim_(x->oo) (x^2-4)/(2x-4x^2)=lim_(x->oo) x^2(1-4/x^2)/(x^2(2/x-4))=(1-lim_(x->oo)4/x^2)/(lim_(x->oo)2/x-4)=(1-0)/(0-4)=-1/4`