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Consider the following three functions. f1 = 10n f2 = nlogn f3 = n√n Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

Consider the following three functions. f1 = 10n f2 = nlogn f3 = n√n Which one of the following options arranges the functions in the increasing order of asymptotic growth rate? Correct Answer f<sub>2</sub>, f<sub>3</sub>, f<sub>1</sub>

Explanation:

f1 = 10n 

By taking log

f1 = n× log(10)

f2 = nlogn

By taking log

f2 = logn × logn

f3 = n√n

By taking log 

f3 = √n × logn 

asymptotic growth rate: f2 < f3  < f1

Therefore option 4 is correct

Important Points

Take n equal to very large number  to verify the result 

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