Someone please help me ASAP on these problems in Real Analysis.
1.> Find Lim supXn (upper limit) and Lim infXn (lower limit)
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
(0, infinity), then Lim f'(x) = 0 (i.e. 1st derivative of f=0)
Please somene help.