Given any o :> 0, we consider the following nonlinear equation: Our goal is to nd a. fast xed-point iteration that converges to the root J." = o. a) Consider the following iteration: It\" = iii-1'01 9(1) == 13 + I '13- [2) Show that I\" = a is the only xed-point of this xE'd-point iteration. For an arbitrary initial point mu 5% a, will this iteration converge to 1-" = {1? Explain why! Hint: Write r} o in the form 9(1) o = h[;r)(:r o) for some suitable function in. 'What can you say about |h{1.-)| or \"ak\"? b) Uoneider the following xed point iteration: Ik+1 = irt}. it) := I + . {3) Show that :r\" = a is the only xed point of the mapping 3}. Show that x) 2 a for all .'r } 0. - Show that the iteration [3) converges to :r" = o for any initial point In E (0,00). What is the rate of oonvergmiee