Posted by MW on .
lim x approaches 0
[1/x *((1/(sqrt(1+x))1)]
It will be easier to understand if you write it out..
How would I algebraically do this? (The answer is 1/2)
Help please?

Pre Calc 
drwls,
I suggest you use L'Hopital's rule. The limit of the ratio of (1/(sqrt(1+x))1)] to x is the ratio of the derivatives of numerator and denominator.
The derivative of x (the denominator) is 1.
The derivative of 1/(sqrt(1+x) 1 at x = 0 is (1/2)(1+x)^3/2 = 1/2
So the limit is (1/2)/1 = 1/2