Homework Help: Limit problem

1. Sep 21, 2008

Nowshin

1. The problem statement, all variables and given/known data

lim (1/sqrt(x+a)-1/sqrt x)
x->0

2. Relevant equations

None

3. The attempt at a solution

Too many too be listed :P

2. Sep 21, 2008

Pacopag

Sometimes, a limit just doesn't exist. But you have to prove that it doesn't. I'm sure that you've determined that the first term is fine. So your problem arises in the second term. I think that a proof by induction using L'Hospitale's rule should do it (I mean repeated applications of the rule just make things worse and worse).

3. Sep 21, 2008

Attempted solutions: "Too many too be listed "

Aaah, there's a (not the, as there may be others) rub - you need to show something you've tried before you receive any help. What types of things have you attempted?

4. Sep 22, 2008

Nowshin

I tired using the L'Hospitale's rule, but it didn't help. The damned "x" won't go away!Then I tired to rewrite it as

1/sqrt(x+a)-1/sqrt x) = (sqrt x- sqrt(x+a) )/sqrt(x(x+a))

and tried multiplying both the numerator and the denominator with (sqrt x + sqrt (x+a) ).That didn't work either.

BTW, the answer is supposed to be a/2 according to my book. Are you sure? The answer might be wrong, though.

Last edited: Sep 22, 2008
5. Sep 22, 2008

danago

Unless im missing something, but i dont see how it can possibly be a/2.

The function isn't defined for all x<0, so the left hand limit wouldnt exist?

6. Sep 22, 2008

Nowshin

The book I use is quite crappy and has some wrong answers. :P

7. Sep 23, 2008

Nowshin

I contacted my teacher and it seems Pacopag was right, the limit really doesn't exist. :D