1. Please find the complexity of the following functions in terms of the Big-Oh notation.
(a) f(n) = 64n
(b) f(n) = 1000000
(c) f(n) = 3n 2 log n + 6n + 100000
(d) f(x) = 5x 3 + log x + 66
(e) f(n) = 10 log2 n + 2n
2. Please order the following functions by growth rate:
n, √ n, n1.5 , n2 , n log n, 3/n, n log log n, 2 n , 6, n3 .
3. Prove that 2n 2 + 3 = O(n 2).