Order the following functions according to their order of gr

Order the following functions according to their order of growth from lowest to highest. Ties if any must be clearly stated. Thank you!

(a) log 2 n 10   (b) 6 n   (c) log 2 n   (d) ( n + 1000)! (e) 3 n (f) 1 . 9 3 n (g) n 8 1000 (h) n 6000 (i) 0 . 0001 n 2 + 10 5 n (j) n log n

Solution

log 2 n < 6 n < 3n= 1 . 9 3 n = n 8 1000 = n 6000(O(n)) < n log n < 0 . 0001 n 2 + 10 5 n < n 8 1000 < log 2 n 10 < ( n + 1000)!