Homework Help: Find the limit

1. Sep 4, 2008

andrewjacobs

1. The problem statement, all variables and given/known data
2. Find the limit.
lim
x->0
for
1-sqrt(x^2-1)
---------------
x^2

2. Relevant equations
No clue, that's why I am asking.

3. The attempt at a solution
I inverted the signs and multiplied by sqrt(x^1+1)+1
So:
sqrt(x^2+1)-1 sqrt(x^2+1)+1
--------------- * --------------
-(x^2) sqrt(x^2+1)+1
and came up with
x+1-1
----------------------
-(x^2)*sqrt(x^2+1)+1
which gave me
0/2

I am sure this isn't correct, but I do not know were I messed up.

2. Sep 4, 2008

Dick

(sqrt(x^2+1)-1)*(sqrt(x^2+1)+1)=(x^2+1)-1. Now isn't it? Not (x+1)-1. As (a+b)*(a-b)=a^2-b^2?

3. Sep 5, 2008

Math Man900

when i graphed it, i found the answer to be
infinity - infinity*i
or
(1-i)*infinity
none of those answer sound like what a teacher would be looking for, so i would guess the answer is either "limit does not exsist" or you copied the problem wrong

4. Sep 5, 2008

HallsofIvy

Your method is perfectly good. You algebra needs some work!
First you can't just change the x^2- 1 inside the square root into x^2+ 1 by "inverting the sign". Second, (1- sqrt(x^2+ 1))(1+ sqrt(x^2+ 1))= 1- (x^2+11)= -x^2.

In any case, if you just let x= 0 in the original form, you get (1- i)/0. Since the numerator is not 0, that limit does not exist.