Proof on Differentiation and Limit.

Someone please help me ASAP on these problems in Real Analysis.

1.> Find Lim supXn (upper limit) and Lim infXn (lower limit)

n-->infinity n-->infinity

where Xn is a recurrent sequence, X1= 1/2 and Xn+1= 1-(Xn)^2

2.> Let f(x) be twice continously differentiable on (0,infinity). Prove that if

Lim f(x) exists and f''(x) (i.e. 2nd derivative of f) is bounded on

x-->infinity

(0, infinity), then Lim f'(x) = 0 (i.e. 1st derivative of f=0)

x-->infinity

Please somene help.