Answer: Limit of (1 - (x^.5))/(1 + (x^.5)) as x Approaches Neg. Infinity

[Val-]

So, I've been mulling over this limit problem for far too long. I feel completely at a loss and refuse to accept my answer of "no limit" or "undefined" regarding the following:

The limit of (1- (x^.5))/(1+(x^.5)) as x approaches NEGATIVE infinity.

Someone care to elaborate on what is actually going on here? As I see it, even multiplying by the conjugate, I still end up with an x variable under a radical and so, the square root of any negative number is imaginary. Can such a number "approaching negative infinity" or "x" can also be a positive number, but moving in the negative direction? Being that as it may, I'm trying to keep the answer within the context of real numbers. So, what is the answer?

-Val-

 

[Dick]

You can't keep x^(0.5) for x negative in the context of the real numbers. Face it. Once you gotten over that, it certainly has a limit in the complex numbers, regardless of branch choice. The answer is -1.