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Growth Rate of Functions : Limits, Infimum, Supremum, Asymptotic Upper Bound, Asymptotically Negligible, Asymptotic Lower Bound, Asymptotically Dominant and Asymptotically Tight Bound

Function A Function B
------------ -----------
n^1/3 6 log(n)

is A=O(B) ? Yes/No
is A=o(B) ? Yes/No
is A=Big Omega(B) ? Yes/No
is A=Small Omega(B) ? Yes/No
is A=Theta(b) ? Yes/No

Also the same for the following pairs.

n^2*2^n 3^n

(n^2!) n^n

n^2/log n n log (n^2)

(log n)^ log n n/log(n)

Would appreciate your help. Please be detailed.

Thanks.

Solution Summary

Growth rate of function pairs is analyzed with respect to Asymptotic Upper Bound, Asymptotically Negligible, Asymptotic Lower Bound, Asymptotically Dominant and Asymptotically Tight Bound. The solution is detailed and well presented.

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