h5 - [40] Homework 5: Big O, . [10] Select the best...

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[40] Homework 5 : Big O, Ω . [10] Select the best “big Oh” notation for each expression. Justify by showing the constants c and n 0 . Note that f ( n ) = O ( g ( n )) if there are constants c > 0 and n 0 > 0 so that for all n n 0 we have | f ( n ) | ≤ c · g ( n ). 1. 100 n + log n . 2. (5 n + 1) 3 + 1000 n 2 . 3. n n 3 + log 5 n . 4. n 3 + n + n + log n . [10] Show the following: 6 n 2 log n 2 n = Θ( n 2 log n ) 6 n 2 + n n log 6 n + 1 = Θ p n log 6 n P n s i =1 i 2 = Θ( n 3 ) [10] Is (log n ) 3 = O (log n 3 )? Justify your answer?
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