?17E Give a big-?O? estimate for (x ? ?2 + ?? log?? 3) • (2? ? + ?x?3).

Solution: Step-1: In this problem we need to find a big-O estimate for (x + x(log x) ) · (2 + x ) x 3 Note: Let us consider f and g are functions from the set of integers to the set of real numbers. The estimate value can be said that f(x) is O(g(x)) if there are constants C and k such that |f(x)| C|g(x)|, where x> k.The constants C and k are called the witnesses to the relationship. The definition of f(x) is O(g(x)) says that f(x) grows slower than some fixed multiple of g(x) as x grows without bound. Step-2: 2 3 x 3 Consider, f(x) = (x + x(log x) ) · (2 + x )………….(1) Assume that x >...