need math help. quickly. as in "this is due tommorow". oh, and it's calc 1.

[Kitsune Ascendant]

the book wants me to find the limit of
(1/(x*(x+1)^(1/2))-1/x, (read: 1 divided by x times the square root of (x+1), minus 1/x) as x goes to 0.

after futzing around with it a bit, I've got it at the point where all I have is
[(x-1)^(1/2)-1]/x. and I can't go any further. I don't see any way to factor an x out of the numerator. and I don't see any way to remove or "change" the x in the denominator to something where the denominator evaluated at 0 is not 0.


any help would be much apreciated.

[insanekaosx]

In a worst case scenario, claim the answer is x-1 and hope for the best

No, actually, if I remember correctly, and I probably don't, there should be something about multiplying be a reciprocal or something to get rid of thigns.... >> Math was never my strong point, but I can try ^^;;

[Supercheese]

Erm, I got -1/2 (negative one-half)...

So, it makes out to be:

1 / (x * sqroot(x+1)) - (1/x)

combine with common denominator:

- sqroot(x+1) + 1 = 0
x * sqroot(x+1)

Multiply both sides by sqroot(x+1)...

(- sqroot(x+1) +1) / x = 0

Wait, limit rules can be done graphing/solving and looking at x approaching 0...

So, not sure why I did all this work, maybe makes it easier to graph/solve >.>  ...

*Ahem* When you *do* solve for x, it's undefined at 0, hence the limit. When x = .0000001, y is really, really close to .5.  When x = -.0000001, y is also really, really close to .5. Isn't that all you need for your proof?

[Kitsune Ascendant]

Erm, I got -1/2 (negative one-half)...

So, it makes out to be:

1 / (x * sqroot(x+1)) - (1/x)

combine with common denominator:

- sqroot(x+1) + 1 = 0
x * sqroot(x+1)

Multiply both sides by sqroot(x+1)...

(- sqroot(x+1) +1) / x = 0

Wait, limit rules can be done graphing/solving and looking at x approaching 0...

So, not sure why I did all this work, maybe makes it easier to graph/solve >.>  ...

*Ahem* When you *do* solve for x, it's undefined at 0, hence the limit. When x = .0000001, y is really, really close to .5.  When x = -.0000001, y is also really, really close to .5. Isn't that all you need for your proof?

for a previous chapter. this one, we're supposed to do it algebraically, so pleace continue as I'm still at a loss.

[Supercheese]

come back! that's the answer!

I'm here...

The definition of limit (I have it saved on my calculator text editor):

L is the limit of f(x) as x approaches c if and only iff L is the one number you can keep f(x) arbitrarily close to just by keeping x close enough to c, but not equal to c.

If that makes sense.

[Castle Pokemetroid]

What grade are you in? I'm in the 8th grade that looks hard. Or it's the fact that math questions like that makes more sense and looks more better if it's on paper.

I'd help if that didn't look so advance.

[Supercheese]

So, algebraically, eh? Then you'll need all those deltas and epsilons.

Ok, should be purdy simple (but isn't. blast): solve this equation:

L = limit, e = epsilon

L - e < f(x) < L + e

If you don't know what I'm talking about, then...

"L is the limit of f(x) as x approaches c if and only if for any positive number epsilon, no matter how small, there is a positive number delta such that if x is within delta units of c but not equal to c, then f(x) is within epsilon units of L."

EDIT: Wait, I'm missing something...

Gah, I can't quite remember something critical... it eludes me...

[Kitsune Ascendant]

HAH! found it!

I was going about it the wrong way. here's what I did:

multiply 1/x by sqrt(x+1)/sqrt(x+1) to get a common denominator, resulting in 1-sqrt(x+1)/(x*sqrt(x+1))

multiply the result above by [1+sqrt(x+1)]/[1+sqrt(x+1)], which, after factoring out an x left me with -1/(sqrt(x+1)+x+1), which is exactly -1/2 when x is equal to 0.

[Supercheese]

... that works too. Just as a point of interest, I found this... http://math.hws.edu/javamath/config_applets/EpsilonDelta.html

Sorry if I wasn't much help... =/   I did get the answer right, though.