undersetx→-∞lim(x^3-x)/(√(1+x^6)) is equal to

$y=-x$

$\underset{x→-∞}{\lim}\frac{x^3-x}{\sqrt{1+x^6}}=\underset{y→∞}{\lim}\frac{-y^3+y}{\sqrt{1+y^6}}=\underset{x→-∞}{\lim}\frac{y^3\left(-1+\frac{1}{y^2}\right)}{y^3\sqrt{\frac{1}{y^6}+1}}=\frac{-1}{1}=-1$