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In proving big-oh and big-omega bounds there is a relationship between the c that is used and the smallest n_0 that will work (for 0,
In proving big-oh and big-omega bounds there is a relationship between the c that is used and the smallest n_0 that will work (for 0, the smaller the c, the larger the n_0: for big-omega, the larger the c, the larger the n_0). In each of the following situations, describe (the smallest integer) n_0 as a function of c. You'll have to use the ceiling function to ensure that no is an integer. Your solution should also give you a lower bound (for big-oh) or an upper bound (for big-omega) on the constant c. (a) Let f(n) = 2n^3 + 7n^2 and prove that f(n) elementof O(n^3). (b) Let f(n) = 2n^3 - 7n^2 and prove that f(n) elementof Ohm(n^3). (c) Let f(n) = 3n^3 + n^2 and prove that f(n) elementof O(n^4)
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