(a) Show that the function f NZ defined by f(n) n is not O(n) (b) The function g R R defined by g(x) x 5 5 (x 4 x 2 1)logx 9 is big O of which one of the following functions (i) logx 9 (ii) 5 (iii) x 4 (iv) x 5 (v) x 4 logx 9

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Question: (a) Show that the function f : NZ + defined by f(n)=n! is not O(n). (b) The function g : R + R + defined

(a) Show that the function f : NZ⁺ defined by f(n)=n! is not O(n).

(b) The function g : R⁺R⁺ defined by g(x)=x⁵+5!+(x⁴+x²+1)logx⁹ is big-O of which one of the following functions? (i) logx⁹ (ii) 5! (iii) x⁴ (iv) x⁵ (v) x⁴logx⁹.

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