In this exercise, we want to verify computational rules involving the asymptotic big-O notation. a) Show that (1 + O(x) ) (1 + O(x)) = 1+ O(x) for a - 0. The precise meaning of this statement is that if f is a function satisfying f(x) = (1 + O(x))(1 + O(x)) as r + 0, then f also satisfies f(x) = 1 + O(x) as r - 0. b) Verify that (1 + O(x)) = 1+ 0(x) for r - 0. Hint: The formula for the geometric series, Spo 1-, for |r|