Question

How do you find the limit of `(3 x^4 + 4) / ((x^2 - 7)(4 x^2 - 1))` as x approaches infinity?

Answer 1

`3/4`

Explanation:

`(3 x^4 + 4) / ((x^2 - 7)(4 x^2 - 1))=x^4/x^4(3+4/x^4)/((1-7/x^2)(4-1/x^2))` so

`lim_(x->oo) (3 x^4 + 4) / ((x^2 - 7)(4 x^2 - 1)) = lim_(x->oo)(3+4/x^4)/((1-7/x^2)(4-1/x^2)) = 3/4`