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Consider the following three functions. f1 = 10ⁿ, f2 = n^(log n), f3 = n^(sqrt(n)) Which one of the following options arranges the functions in the increasing order of their growth rate as n tends to infinity?

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

Correct answer: f2, f3, f1

Solution

As n approaches infinity, f2 grows at a rate of n raised to the logarithm of n, which is slower than f3 (n raised to the square root of n) but faster than f1 (10 raised to the power of n). Therefore, the correct order of growth rates is f2, f3, and then f1.

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