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Example 3: The Growth of Functionsand Asymptotic notation a) Show that x is O(x )but that r is not O(x b) Give as good a big-O estimate as possible for each of the following (A formal proof is not required, but give your reasoning): log,n! 7n n +nlo 3n2 +2n+4 . (n log, (log,n) 2 42 c) Which of the functions in part b) above has the fastest growth rate? d) Show that if f(x) is Ollog, x)where b>1, and then f(x) is Olog, x) where a>

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