You just need to apply it once more.
(sin(sqrt x))/(2 sqrt x) -> 1/2x^(-1/2)sin(sqrt x) / x^(-1/2) simplifies to 1/2cos (sqrt x).
Forgive me if the details aren't right, but I'm pretty sure the idea is there.
I have to use l'hopital's rule to find each limit:
1. lim x approaching 0 from the right of
(1-cos(sqrt x))/x
Since this is a 0/0 form I use l'hopitals rule. making it:
Lim x approaching 0 from the right of (sin(sqrt x))/(2 sqrt x).
Again this is a 0/0 form but if I just keep applying l'hopital's rule it always comes up with a 0/0 form. How do I solve this?