For each of the following functions, give the least integer n such f(x) is O(xⁿ).

a)f(x) = 4x³ + x²log x

b) ) f(x) = 2x² + x³log x + 3

c) ) f(x) = 4x³ + (log x)⁴ + x

d) f(x) = 3x⁵ + (log x)³

e) f(x) = (2x⁴ + x² + 1) / (x³ + 1)

f) f(x) = (x⁴ + 3x² + 1) / (x² + 1)

g) f(x) = (3x⁴ + x³log x) / (x⁴ + 1)

h) f(x) = (2x³ + x²log x) / (x + 1)