help please 4) For each of the following pairs of functions, either f(n) is in O(g(n)), f(n) is in 22(g(n)), or f(n)(g(n)). For each pair, determine which relationship is correct. Justify your answer.(a) f(n) = log n²; g(n) = log n+ 5.(b) f(n)=√n; g(n) = log n².(c) f(n) = log2"; g(n) = log n.(d) f(n) = n; g(n) = log n.(e) f(n) = n log n+n; g(n) = log n.(f) f(n) = log n²; g(n) = (log n)².(g) f(n) = 10; g(n) = log 10.(h) f(n) = 2¹;(i) f(n) = 2;g(n) = 10n².g(n) = n log n.g(n) = 3¹.g(n) = nº.(j) f(n) = 2¹;(k) f(n) = 2";

1)f(n)=log(n^2)=2*log(n), g(n)=log(n)+5So, by limit theormf/g=2/(1+5/log(n))So, for n tending…

Answered: 4) For each of the following pairs of…

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4) 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. (a) f(n) = log n²; g(n) = log n+ 5. (b) f(n) = √n; g(n) = log n². (c) f(n) = log2"; g(n) = log n.