Answer Happy

This problem is already solved but I do not understand how to do
it. Please walk me through each step of it, I've had alot of
trouble understanding this class.
Problem 2.2: Let g(n) = n2 + n°(1+(-1)"). Are the following identities true? Use the definition of N, O and o, respectively, to justify your answers in (a), (d) and (e). = (a) g(n) = N2(nº) Solution: True We have that 1.n? < g(n) holds for every n > 0. (b) g(n) = N(n3) Solution: False. Because for odd n, g(n) = n2, there are no constants c > 0 and no > 0 such that for every n > no, = cnº < g(n). = (c) g(n) = O(n) Solution: True For every n > 0 we have g(n) < n2 + 2n3 < 3n3. = Thus, g(n) = O(nº). (d) g(n) =0(m2) Solution: False. Since for every even n, g(n) = n > no, = n2 + 2n', there are no constants c > 0 and no > 0 such that for every g(n) <cna.