2. (15 pts) 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)). Determine which relationship is correct and briefly explain why. Hint : use Lopital's rule a. f(n)=log2;g(n)=logn+5 g(n)f(n)=0somefinite,nonzeroposifiveconstantf(n)=0(g(n))f(n)=(g(n))f(n)=(g(n)) logn+5logn2=limnlogn+52lognx(ln(2)1ln(2)x2=12=2 n)=(g(n))x(ln(2) Which relationship is f(n)