3.3 Consider the function f (x) in Example 3.3.

(i) Suppose that ap, bq are nonzero. Show that as |x| → ∞, f (x) = o(1) if p < q, f (x) = O(1) if p = q, and 1/f (x) = o(1) ifp > q.
(ii) Suppose that b0 = 0. Show that as x → 0, f (x) = O(1) regardless of p and q.