1. Given that F(N) = 3 N2 + 5 N3 + log (N), which of the following equalities holds? (CHECK ALL OPTIONS THAT ARE CORRECT) a) F(N) = O(N3 ) b) F(N) = o(N4 ) c) F(N) = (N3) d) F(N) = (N3)

2. Assume that F(N) < G(N) for all N< C, whereas F(N) > G(N) for all N>C , (C is a positive integer). Then,

a) O(F(N) + G(N)) = O(F(N)) b) O(F(N) + G(N)) = O(G(N)) c) Both are correct.

3. True or False? a) O(log N^K) = O(log N) b) (log N^K) = (log N).

4. Which of the following statements is a conclusion of lim[g(n)/f(n)] as n-> = 0?

g(n) = O(f(n))

g(n) = o(f(n))

g(n) = (f(n))

g(n) = (f(n))

5. Which of the following statements is a conclusion of lim[f(n)/g(n)] as n-> = lim[(g(n)/f(n)] as n-> ?

g(n) = O(f(n))

g(n) = o(f(n))

g(n) = (f(n))

g(n) = (f(n))

PLEASE PROVIDE EXPLANATION FOR EACH ONE