Hey guys,

i'm working on real analysis and i'm stuck on these 2 questions:

1) Prove that the annulus A = {z belongs to R2| r <=|z|<=R} (where R>r>0) is connected.

2) f: R -> R is differentiable

Suppose there exists L < 1 such that f'(x) < L for all R

(a) Prove that f has a unique fixed point

(b) Show by example that (a) fails if L = 1

Thanks alot guys!