Work the following problems. Write your solutions in order on one side of the paper and very neatly in ink. Use this assignment sheet as the cover page and staple pages 1. (12 pts) Find the big-O estimate for each of the functions below. Get the bound in terms of a smallest single term such as r"n or n. Specifically, find least integer n, and smallest numbers C and k and prove your estimate. Provide plots of the function and the bound on the interval of the big-O bound (a)2 log )(log)(3 log r 10e( 2) (b) (2 + 2)( 3 + 3*) (c)5log(20) 2. (8 pts) Prove by induction that for n21 2k = (n 1)2n + 1 +2 1 Label each step very carefully and do not skip steps. This can be proven in other ways. The problem here is to do this by induction to demonstrate you know how to apply this particular technique