(3) (Understanding asymptotics) (25 points) (a) (15 points) Order the following functions according to their rate of growth. Specif- ically, group the functions into equivalence classes such that functions f and g are in the same class iff f E (g), and then order the equivalence classes from slowest to fastest growing. For each successive pair of functions (f, g) in your order, state the relationship between f and g, namely either fe O(g) or fe 0(g). n! [Inn]! m2 (Inn)2 ln(n!) 22 In Inn mln Inn Vinn 2lnn (In n)Inn 41 n 21 nlnn (Hint: First form a rough initial order of the functions, and then use insertion sort on this list to obtain the final order. To determine the relationship between two functions, take a limit of their ratio, or use the list of asymptotic properties given in class.)