Question

What is the limit of `(1-x^2)/(x^3-x+1)` as x approaches infinity?

Answer 1

We have that

`lim_(x->oo) (1-x^2)/(x^3-x+1)=lim_(x->oo) (x^2*[1/x^2-1])/(x^3*[1-1/x^2+1/x^3])=lim_(x->oo) ([1/x^2-1])/(x*[1-1/x^2+1/x^3])=0`