UFF

So I have this calculus class, and I was assigned this problem.

I've been stuck on it for.... 4-5 hours or so, and was curious if anyone here has the mathematical skill to actually explain it to me. I feel like I'm just overlooking something stupid. I've asked a couple of people, and I'm really starting to get annoyed.

Here's the problem:
(At school, had to use MS paint)

So, (in case you can't read that), it says the limit as x approaches 0 of f(x) of ([1/sqrt(x+1)]-1)/x

...You do realize that MS Paint has a "text" tool, right?

Anyways, just put it into Wolfram Alpha, came out as:

(no result found in terms of standard mathematical functions)

Fffffffffffffffffffucking calculus.

Are you sure you're reading it right? Did you copy it from somewhere, and are you sure you copied it right?

Basically, substitute 0 for x and you end up with 0/0. This is patently retarded.

You cant substitute 0 or -1 for x in that problem due to impossibility of diving/taking square root of zero.

This is quite special as I recall. Basically, try drawing that on a coordinate system and you will get a huge fucking gap where those numbers ought to be.

What Alex said. The impossible substitutions are the vertical asymptotes. Still not sure what you're supposed to be finding, though.

The left... I'm not sure.
f(x) = (1/sqrt(x+1) - 1) / x...
Please clarify the left text.

Means "the limit, as x tends to 0".

To correct myself, you can take square root of zero, just not that of a negative number.

Imaginary numbers.

Meet your new God i.

Found out you have to rationalize the numerator and then do some crap to rationalize the denominator. Came out with -.5 as the answer. >_<