1. [HM01] What is limn→∞ O(n− 1/3)?
2. [M10] Mr. B. C. Dull obtained astonishing results by using the “self-evident” formula O(f (n)) − O(f (n)) = 0. What was his mistake, and what should the righthand side of his formula have been?
3. [M15] Multiply (ln n + γ + O(1/n)) by , and express your answer in O-notation.
4. [M15] Give an asymptotic expansion of , if a > 0, to terms O(1/n3).
5. [M20] Prove or disprove: O(f (n) + g(n)) =