In: Advanced Math
How to determine whether the following statements about big-O notation are true or false?
(a) Let f(n) = √ n log n − 4, then f(n) = O(n^ 2)
(b) Let f(n) = 4 n + 2 log^ 2 (n), then f(n) = O(log^ 2 (n))
(c) Let f(n) = 5 √ n + 2, then f(n) = Ω(log^ 4 (n))
(d) Let f(n) = 5 n^ 2 + 5 n log n + 4, then f(n) = O(n^3 )
(e) Let f(n) = 2 log^2 (n) + 5√ n + 7, then f(n) = Θ(√ n)