Question

\[lim_{x rightarrow -\ infty} \sqrt{9x^6 - x} / (x^3 + 5) /]

Answer 1

\[\[\lim_{x \rightarrow -\ \infty} \sqrt{9x^6 - x} / (x^3 + 5) /] \]

Answer 2

How do we deal with the expression within the square root?

Answer 3

pull out x^6 from the radical and it becomes x^3\[\lim_{x \rightarrow -\infty}x^3\sqrt{9-1/x^5}/x^3(1+5/x^3)=\sqrt{9}/1=\pm 3\]
I forget whether to use the negative or positive root, but I want to say use -3 because we are going to -infinity. Not sure though...