# Math Help - Mystifying limit

1. ## Mystifying limit

Hey, I was wondering if someone might give me a hand with taking a limit; I'm attaching a pdf version of the limit and my solution attempt. Essentially, what I've done is multiply by the conjugate and then simplified as far as possible - at which point someone involved has obviously made a mistake, since the key claims that the correct answer is -2. At the same time, I can't help but notice that if you were to change the sign before the last x^3 term, you'd get +2, tempting me to suggest that I'm not the one at fault here. But yea, anyone wanna give me a hand figuring out where I'm going wrong here? Thanks in advance!

2. ## Re: Mystifying limit

Let $x<0$. Then $x^6>0, \sqrt{x^6}>0$, but $x^3<0$. Hence, $\sqrt{x^6} = -x^3$.

3. ## Re: Mystifying limit

That... makes a ridiculous amount of sense. Thanks a lot!