The complexity of a computer algorithm is the number

of operations or steps the algorithm needs to complete its tasks assuming there are

n pieces of input $($for example, the number of steps needed to put n numbers in

ascending order$).$ To compare the rates of change of two functions, you can find

limn$->\backslash$infty f $($n$)$

g$($n$).$

Four algorithms for doing the same task have complexities of A: n$3/2,$ B: n log$2$ n$,$

C: n$($log$2$ n$)2,$ and D: $$n log$2$ n$.$ Rank the algorithms in order of increasing ef$-$

ficiency for large values of n$.$ Graph the complexities as they vary with n and

comment on your observations. Show all the work that leads to your answer.