3. (a) (10 points) Sort the following functions from asymptotically least to greatest: that is, make a series of a statements like "f3 = o(fi), fi = e(fa), f4 = 0(fs), fs = o(f9), ..., S8 = (17)", where cach function is either o or of the next. All logs are base 2 unless otherwise specified. i. fi = (log nalogn ii. f2 = n(log log n) / log n iii. 13 = log2 n iv. S4 = (logn) v. /5 = log5 (12") vi. fo = 6 vii. f7 = (7")/(zlog ) viii. fs = n/(8 log na) ix. f9 = (9ru) long log in (b) (5 points) Give an example of a function g that would not fit into the order above: that is, one for which, for some i, fi + 0(9), fi o(g), and g * o(fi)