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Question: 1 show that 12or fork nen and k n 2...

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1. Show that 12Or+) fork, nEN and k, n 2. Show that for all real numbers a and b with a > 1 andb > 1, iff(x)-O(log,x), then 3. Show that the two functions log(2 ) and log(r) are of the same order (recall that same 4. Letf(x), g(x), and h(x) be three functions such that,f(x)-6(g(x)) and g(x) = Θ(h(x)). 5. Arrange the functions 2100 , 27, 2.22. , ni g,n10g n log log n, mv2 , п(log n)v2 , and f (x)O(loga x). order is established using O). Prove that fr)(h(r)). no 1/3 n a list so that each function is big-O of the next function. Briefly justify your answer.
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