State and prove the correct relationship O o between the

State and prove the correct relationship (O, o, , , ) between the functions f(n) = n² log n + 2n and g(n) = n³ + 4n log n.

O-notation : is tightest upper bound.. f(n) is said to be O(g(n)) where there exist a constant k>0, where f(n)<=k*g(n) for n>n0

o-notation: is upper bound not tight.. f(n) is said to be o(g(n)) , for every constant k>0, f(n)<k*g(n) for n>n0

big-OMega- notation: is tightest lower bound.. f(n) is said to be big-OMEGA(g(n)), for a constant k>0, f(n)>=k*g(n),n>n0

small-OMEGA- notation: is a lower bound not tight.. f(n) is said to be small-OMEGA(g(n)), for every constant k>0, f(n)>k*g(n),n>n0

theta notation: it is average case, f(n) is said to be theta(g(n)), for two constants k1 and k2 , k1*g(n)<=f(n)<=k2*g(n)

given

f(n) = n2 logn+2n and g(n) = n3+4n logn

for n>1 the growth rate of g(n) is greater than the growth rate of f(n)...

so.. for every constant k>0, k*g(n) is always greater than the f(n), for n>1

hence f(n) = o(g(n)) and

g(n) = small-OMEGA(f(n))