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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?


1. f1 , f2, f3
2. f2, f1, f3
3. f3, f2, f1
4. f2, f3, f1

1 Answer

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Best answer
Correct Answer - Option 4 : f2, f3, f1

Explanation:

f1 = 10

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: f< f3  < f1

Therefore option 4 is correct

Take n equal to very large number  to verify the result 

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