Question

How do you find the limit of `(2x^2 + 1) /( (2-x)(2+x))` as x approaches infinity?

Answer 1

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

Explanation:

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

Divide by highest power of x

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