Question

What is the limit of `(sqrt (9x^6 - x) ) / (x^3 + 4)` as x approaches negative infinity?

Answer 1

The limit is `3`.

Explanation:

`lim_{x->-oo}(sqrt(9x^6-x))/(x^3+4)=lim_{x->-oo}(sqrt(x^6(9-1/x^5)))/(x^3(1+4/(x^3)))=`

`=lim_{x->-oo}(x^3*(sqrt(9-1/x^5)))/(x^3(1+4/x^3))=3/1=3`