Find the least integer n such that f(x) is O(xn) for each of these functions.a) f(x) = 2x3+x2logx________________b) f(x) = 3x3 + (logx)4________________c) f(x) = (x4 + x2 + 1)/(x3+ 1)________________d) f(x) = (x4 + 51ogx)/(x4 + 1)

SolutionStep 1In this Problem, we have to find the least n such that f(x) is O()a) f(x) = Here log x is less than x so it grows slowly as compared to x, is less than so it also grow very slowly as compared to , So the first term influence.Hence, the function is O( ).So, n 3 = +Here, n = 3, C = 3 and k = 1Step 2b) Here,log x is less than x so it grows slowly as compared to x, is less than so it also grows very slowly as compared to , So the second term influence.Hence, the function is O().So, n 3 = = 4Here, n = 3, C = 4 and k = 1Step...