Answer the following question using a step-by-step procedure. Include all necessary steps and comments, showing all your work throughout the solution. The material is based of zybooks and what was lectured during class time. Thank you and will rate afterwards!

1. (25 pts) For each of the pairs of functions f and g given in the table below, determine if f(n)=0(g(n)), 2(g(n)), Olg(n), olg(n), or w/g(n)) and justify your answers. More precisely, do the following for each pair of the given functions: - if you decide f(n) = O(g(n)) / 2(g(n)), then find a constant c>0, where f(n) = cg(n)/ f(n) cg(n) for all n21. - if you decide f(n) = 0(g(n)) / w(g(n)), then show the limit of f(n)/g(n) is 0/-0, where n approaches oo. Conclude that f(n) = O(g(n)) if you decide that f(n) is both O(g(n)) and 2(g(n)) g(n) f(n) 2n-1 n1.5 n2 log? n n log (na) 100n n log n n3 n log (log n) 2n 2n-1