Question 2. Consider the sequence (a,) given by a; = a, a,+1 = a,(2 a,) for n > 1,where a R. (a) Find all the values of o R such that (a,) converges, and for each of these values of , find the limit lim a,. (As part of your answer, you should find the values of a such that TE+ OO (a,) diverges.) (b) Let f : R R be a continuous function such that f(z) = f(z(2 z)), for each x R. Prove that f is constant on [0, 2]