(1) Question 3. (15 points. We shall consider the function h given by h(n) = 1g(n!) (for n > 1). That is, h(n) = \sc[= 1500 Prove, from the definition of big-O (without appealing to auxiliary results), that 1. (5p) h(n) O(nIg(n)) 2. (5p) h(n) O(n) 3. (5p) h(n) Sin Ig(n)). (Thus, given 1, also h(n) E O(n Ig(n)).) Hint (for 2 and 3): in the sum on the right of Equation 1, more than of the terms will be > 15(). (1) Question 3. (15 points. We shall consider the function h given by h(n) = 1g(n!) (for n > 1). That is, h(n) = \sc[= 1500 Prove, from the definition of big-O (without appealing to auxiliary results), that 1. (5p) h(n) O(nIg(n)) 2. (5p) h(n) O(n) 3. (5p) h(n) Sin Ig(n)). (Thus, given 1, also h(n) E O(n Ig(n)).) Hint (for 2 and 3): in the sum on the right of Equation 1, more than of the terms will be > 15()