For each of the following pairs of functions, either f(n) is in O(g(n)), f(n) is in (g(n)), or f(n) = (g(n)). For each pair, determine which relationship is correct. Justify your answer, using the method of limits discussed in Section 3.4.5

(e) f(n) = n log n + n; g(n) = log n.

(f) f(n) = log n 2 ; g(n) = (log n) 2 .

(g) f(n) = 10; g(n) = log 10.

(h) f(n) = 2n ; g(n) = 10n 2 .

(i) f(n) = 2n ; g(n) = n log n.

(j) f(n) = 2n ; g(n) = 3n .

(k) f(n) = 2n ; g(n) = n