asymptotic notations calculater

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1) Considering the f (n) and g (n) function pairs given below, the f (n) function f (g (n)), Find out which classes belong to asymptotic classes o (g (n)) and omega(g (n))

a: f(n)= n(logn)^3 , g(n)= n^4/3 b:f(n)= n^logn, g(n)=2^n2


2)Identify the asymptotic classes by solving the recurrence equations given below (Master Theorem will not be used).

a: T(n)= 25T(n/5)+n^2 T(1)= 0

b: T(n)= 3T(n-1)+n T(0)= 0

c: T(n)=5T(n-1)-6T(n-2) T(0)= 0,T(1)=1

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