Question

Order the following functions by asymptotic growth rate.

2n log n + 2n, 2¹⁰, 2 log n, 3n + 100 log n, 4n, 2n, n² + 10n, n³, n log n²

Answer 1

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first divide all the things into two categories 1) polynomial 2) exponential and we know exponential has faster growth than polynomial. now internally sort them according to their power. if you got confused between two , take n=10,100,1000,10000 and substitute value of n and compare the two to find which has faster growth

2¹⁰, 2 log n, 2n = 4n = 3n + 100 log n, 2n log n + 2n = n log n² , n² + 10n, n³,