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

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

Answer 3

\[\left(\frac{\sqrt{-x+9 x^6}}{5+x^3}\right)^2=9+\frac{225-x}{\left(5+x^3\right)^2}-\frac{90}{5+x^3} \]The limit of each x term in the RHS as x->Infinity is zero. The square root of 9 is 3.

From Mathematica:\[\text{Limit}\left[\frac{\sqrt{-x+9 x^6}}{5+x^3},x\to \text{Infinity}\right]= 3 \]