limit of $\sqrt{(x^2+1)/(x^3+1)}$ as $x$ approaches negative infinity $\lim_{x \rightarrow - \infty }  \sqrt{ \frac{x^2+1}{x^3+1} } $
My teacher says that no limit exists, but Wolfram Alpha says the limit is 0. I'm confused.
Any helps are welcome.

The answer depends on the underlying domain of the expression. To see this, you may write
$$\sqrt{ \frac{x^2+1}{x^3+1} } \stackrel{x<-1}{=} \sqrt{-1} \cdot \frac{1}{\sqrt{|x|}} \cdot \sqrt{ \frac{1+\frac{1}{x^2}}{1+\frac{1}{x^3}} } = \begin{cases} \mbox{not defined} & \mbox{ in } \mathbb{R} \\ \pm i \cdot \frac{1}{\sqrt{|x|}} \cdot \sqrt{ \frac{1+\frac{1}{x^2}}{1+\frac{1}{x^3}} } \stackrel{x \to -\infty}{\longrightarrow} 0 & \mbox{ in } \mathbb{C}\end{cases}$$
