Algorithms Analysis & Design, Can I get the answers with the solution method?

I have a hard time asking numbers two and three with their options.

1 Introduction The objective of this assignment is to get some hand-on experiences on different analysis tech- niques covered in the Chapter-2. Moreover, you will explore and implement two algorithms in both recursive and non-recursive fashions and compare their run times in this assign- ment. In essence, the assignment contains four problems with varying marks to assess your analytical ability to determine the algorithmic efficiency through analysis and visualization. Note: throughout the assignment, all logarithms are based 2 logarithms, i.e., log c = log2(2). The maximum grade for this assignment is 20 marks 2 Comparing Functional Growths (Marks: 4) Arrange the following functions in ascending order by their order of growth as n +00: a) ()", logn,23250 1, 0.325n, n,log n, 2log?n, log log n, 22, n0.0001, n log? n, (n 1)!, n3n 4", log n, n! 3 Analysing Asymptotic Bounds (Marks: 3) Prove the following using the definition of asymptotic order notation or using limits. Example: 15n3 + 10n2 + 20 O(n) Hint: Consider C = 15+ 10 + 20 = 45 and no := 1. Then 0 no. a) na + n2 2+cos(n) E O(n) b) 2n? (log n) 12(n(log n)) c) 10n/(n - 10) O(n) d) (n+ 1)10 (n20) e) (10n + 7n + 3) O(n) f) 2(n+1) + 3(n-1) (3") 1