Please help in finding the limits of the following..

1) when limit n -> infinity, find [ sqrt(n^2 + n) - sqrt(n^2 + 1)]

I know we have to use the rationalizing the denominator but I keep getting this is divergent.

2) when limit n -> infinity, find (sqrt(n)[ sqrt(n+1) - sqrt(n)]

3) when limit n -> infinity, find n! / 2^n.

I know we have to use the ratio test in here, but I am stuck at (n+1)/2.