Question: solve 2. Here we will construct the proof that: If lim = 1 0 then f(n) = Q(g(n)) TL OO g(n) Your job is to

solve

2. Here we will construct the proof that: If lim = 1 0 then f(n) = Q(g(n)) TL OO g(n) Your job is to identify some details and finish the proof. Proof Start: Suppose lim an = L 0. Then by definition of the limit we know: n+ coa Ve 0,4ng 0, if n np then Le 0 write down the J part of the statement for = . Solution: (b) We only need one of the inequalities from the right side of the above expression. Rewrite the 4 part of the statement with just that one but solve for f(n). You might have to think a bit to understand which inequality will be the important one. Solution: (c) We have now proved f(n) = Q(g(n)). Which B does the job? Solution

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