Question: 1. List these functions so that each function is big-O of the next function in the list: (log n) 3 , n 3 /1000000, n,

1. List these functions so that each function is big-O of the next function in the list: (log n)3, n3/1000000, n, 100n + 101, 3n, n!, 2nn2. Justify.

2. Is the function f (x) = 8x3 + 5x2 + 7 is W(g(x)), where g(x) is the function g(x) = x3. Show your solution.

3. Show that 3x2 + 8x log x is Q (x2).

4. Give a big-O estimate for f (x) = (x + 1) log(x2 + 1) + 3x2

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