I need help determining the limits of the following problems.

Determine the following limits(if the limit exists otherwise explain why it does not) without using the L'Hospital's rule...

1) Lim [sqrt(4+x) - 2)] / [x]

x->0

2) Lim [ x^2 - 1] / [|x-1|]

x->1

3) Lim [sqrt(x) . cos (1/x) ] ......using L'Hospital's rule...

x->0