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This assignment covers textbook Chapter 3 & Chapter1-2. 1. Function Order of Growth: (20 points) List the 4 functions below in nondecreasing asymptotic order of growth. (lg n)3 lg(2lg (n)) 7n smallest largest Justify your answer mathematically by showing values of cand no for each pair of functions that are adjacent in your ordering. 2, Notation Practice: (30 points, 6 points for each) o,a, Given (for large n): (1)fi(n) E 2((lg n)3) (2)F(n)E O(a3- (3) fs(n)e n1 (4)fln)E e (lg(21g (n)) (a) Draw the arrow diagram associated with the 4 statements above (b) (e) For each statement below, state if it is TRUE (if the statement must always be true, given the assumptions) or FALSE otherwise. In the TRUE case, provide a proof. In the FALSE case, give a counter-example. (b) f(n)E O(fi(n)) (d) fi(n)E O(fa(n) Notation Practice: (15 points) o,a, Let f(n) and g(n) be asymptotically nonegative functions. Using the bas definition of -notation to provethat mas@n).g(n))-e(f(n) + g(n)) 3, Hint max(ftn).g(n)f g(n) This assignment covers textbook Chapter 3 & Chapter1-2. 1. Function Order of Growth: (20 points) List the 4 functions below in nondecreasing asymptotic order of growth. (lg n)3 lg(2lg (n)) 7n smallest largest Justify your answer mathematically by showing values of cand no for each pair of functions that are adjacent in your ordering. 2, Notation Practice: (30 points, 6 points for each) o,a, Given (for large n): (1)fi(n) E 2((lg n)3) (2)F(n)E O(a3- (3) fs(n)e n1 (4)fln)E e (lg(21g (n)) (a) Draw the arrow diagram associated with the 4 statements above (b) (e) For each statement below, state if it is TRUE (if the statement must always be true, given the assumptions) or FALSE otherwise. In the TRUE case, provide a proof. In the FALSE case, give a counter-example. (b) f(n)E O(fi(n)) (d) fi(n)E O(fa(n) Notation Practice: (15 points) o,a, Let f(n) and g(n) be asymptotically nonegative functions. Using the bas definition of -notation to provethat mas@n).g(n))-e(f(n) + g(n)) 3, Hint max(ftn).g(n)f g(n)