Asymptotic Notation


Q41.

Let T(n) be the function defined by T(1) =1, \: T(n) = 2T (\lfloor \frac{n}{2} \rfloor ) + \sqrt{n} \text{ for } n \geq 2.Which of the following statements is true?
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Q42.

Which of the following is false?
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Q43.

Consider the following two functions: g_1(n) = \begin{cases} n^3 \text{ for } 0 \leq n \leq 10,000 \\ n^2 \text{ for } n \geq 10,000 \end{cases}g_2(n) = \begin{cases} n \text{ for } 0 \leq n \leq 100 \\ n^3 \text{ for } n > 100 \end{cases}Which of the following is true?
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Q44.

\sum_{1\leq k\leq n} O(n), where O(n) stands for order n is:
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Q45.

Let f (n) =n^{2} logn and g(n) = n(logn)^{10} be two positive functions of n. Which of the following statements is correct ?
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