For each of the following pairs of functions, either f ( n ) f(n) is in O

For each of the following pairs of functions, either $f\left(n\right)$ is in $O\left(g\right(n\left)\right)$, \( f(n)) is in Ω (g(n)) Ω(g(n)), or f (n) = Θ (g(n) ) f(n)=Θ(g(n)). For each pair, determine which relationship is correct. Justify your answer, using the method of limits discussed in Section 3.4 .5.

(a) f(n) = log n^2; g(n) = log n + 5.

(b) f(n) = √n; g(n) = log n^2.

(c) f(n) = log n^2; g(n) = log n.

(d) f(n) = n; g(n) = log^2 n.

(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) = 2^n; g(n) = 10n^2.

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

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

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