TITLE: Why $\lim_{x\to -\infty} \frac{x^3}{\sqrt{x^6+4}} =-1 $ and not $1$?
QUESTION [8 upvotes]: $$\lim_{x\to -\infty} \frac{x^3}{\sqrt{x^6+4}} $$  When we deal with infinities then 4 is negligible and so the above limit is equal to $$\lim_{x\to -\infty} \frac{x^3}{\sqrt{x^6}} = \frac{x^3}{x^3} = 1$$ but it turns out that this is not equal 1 and it should be -1 , i have no idea why though !

REPLY [3 votes]: If we think graphically before simplification, we can observe that denominator is always positive, and as $x\to -\infty$ value of $x^3\to -\infty$. So It should be -1.