please answer all of parts of the question, each exercise is part of one problem

juoursus/esC215011 Exercise 2.1 Arrange the following expressions by growth rate from slowest to fastest. 4n2 loga n n! 3" 20n 2 log2 n n2/3 nlog2 n n6/ Answer: Exercise 2.2 For each of the following pairs of functions, either f(r) is in O(g(n), f(n) is in (g(n)), or f(n) is in (g(n). For each par, determine which relationships correct. Justify your answer using, for example, t limits discussed in Section 4.7.1.3. (For an example, the first problem is solved for you.) (a) f(n) 10n + 3; g(n)n2 Answer: 10n+3= lim 7l 10 lim 0. By the limit rules of asymptotic notati g(n) (b) f(n)= nlogn + n; g(n)= logn. Answer: (c) f(n) = 10; g(n) = log 10. (d) f(n-2", g(n) = 10n2. (e) f(n)-, 2"; g(n) = 3n , Answer: Answer: Exercise 2.3 Hardware vendor XYZ Corp. claims that their latest computer will run 100 times faster than that of their competitor, Prunes, Inc. If the Prunes, Inc. computer can execute a program on input of size n in one hour, what size input can XYZ's computer execute in one hour for each algorithm with the following growth rate equations? Tt Answer: (b) n2 Answer: (c) Answer: (d) 2