Cauchy sequence & "Fixed" point 1. The problem statement, all variables and given/known data Suppose that f: Rd->Rd and there is a constant c E (0,1) such that ||f(x)-f(y)|| ≤ c||x-y|| for all x, y E Rd. Let xo E Rd be an arbitrary point in Rd, let xn+1=f(xn). Prove that a) f is continuous everywhere. b) (xn) is Cauchy. c) (xn) converges to a limit y. d) Show that y is a fixed point of f ,that is f(y)=y, and that f has exactly one fixed point. 2. Relevant equations N/A 3. The attempt at a solution I proved part a & part b, but I have no idea how to prove parts c & d. Any help is appreciated!