Question

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

Answer 1

I found `1/2`

Explanation:

You can collect `x^2` to get:
`lim_(x->oo)(x^2(1+1/x^2))/(x^2(2-3/x-2/x^2))=lim_(x->oo)(cancel(x^2)(1+1/x^2))/(cancel(x^2)(2-3/x-2/x^2))=lim_(x->oo)(1+1/x^2)/(2-3/x-2/x^2)=` as `x->oo` then `1/x^n->0` so:
`=(1+0)/(2-0-0)=1/2`