Please show me how you sort them.

Sort the following 25 functions from asymptotically smallest to asymptotically largest, indi- cating ties if there are any. You do not need to turn in proofs (in fact, please don't turn in proofs). 42 lg n n2.1 cos(n) + 2 Vign Ign 2lg n vne 1g* 2221 n 12m Ig*(n) (1g* n)lgn (lg n)lgn n1/125 1+ lg lg lg n n5 i2 (1 + 1.15n n1g4n n3/(21gn) nig lg n 12 + [lg lg n 15201 n n1/lg lg n To simplify notation put all the functions in a single column, where f(n) being above g(n) in the column means f(n) = 0(g(n)). If f(n) = O(g(n)), then write f(n) and g(n) separated by a comma on the same line. For example, the functions n?, n, (7), n should be written n n, ) n3 Hint: When considering two functions f(n) and g(n) it is sometimes useful to consider the functions log f(n) and log g(n), since log f(n) = o(log g(n)) implies f(n) = 0(g(n)) (but be careful, the implication does not work in the other direction, and in particular log f(n) = O(log g(n)) does NOT imply f(n) = 0(g(n)))