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Question: to illustrate how the asymptotic notation can be used to...

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To illustrate how the asymptotic notation can be used to rank the efficiency of algorithms, use the relations "\subset " and "=" to put the orders of the following functions into a sequence, where \varepsilon is an arbitrary real constant, 0 < \varepsilon < 1.

nlogn, n^8, n^{1+\varepsilon} , (1+\varepsilon)^n , n^2/logn, (n^2 - n + 1)^4

Do not use "\subseteq". Prove your answers.

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