(a) [10 pts.] Organize the following functions into six groups ( Items in the same group...

 

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(a) [10 pts.] Organize the following functions into six groups ( Items in the same group should have the same asymptotic growth rates (they should be big-O of each other). If a group's label is lower than that of another group, all its growth rates should be slower than those of the group with the larger label (so group 1 should have the slowest growth rates and group 6 should have the fastest growth rates). ,"log", 2log:(), logs (5n), 3n + 10, 4+ (3- 2"), , 405, log2 (n), (b) [5 pts.] Using the definition of big-O, show 4n + 2n = O(n). Give a particular C and no and show why these constants work. 5+8nlog(n) = O(f(n)). You do not need (c) [5 pts.] Identify a function f(n) which has An + to show constants, but should describe how you determined your solution. VI (a) [10 pts.] Organize the following functions into six groups ( Items in the same group should have the same asymptotic growth rates (they should be big-O of each other). If a group's label is lower than that of another group, all its growth rates should be slower than those of the group with the larger label (so group 1 should have the slowest growth rates and group 6 should have the fastest growth rates). ,"log", 2log:(), logs (5n), 3n + 10, 4+ (3- 2"), , 405, log2 (n), (b) [5 pts.] Using the definition of big-O, show 4n + 2n = O(n). Give a particular C and no and show why these constants work. 5+8nlog(n) = O(f(n)). You do not need (c) [5 pts.] Identify a function f(n) which has An + to show constants, but should describe how you determined your solution. VI