3. Using the definition of big-O, show that n = O(2"). Give a particular c and no. 4. Identify a function f(n) which has 3n + 4n² + 3n! = O(n!) and n² = O(n!). O(f(n)). You may use the facts that n =

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Need help on part iii) and iv) 

 

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1. Organize the following functions into six columns. Items in the same column should have the
same asymptotic growth rates (big-O). If a column is to the left of another column, all its
growth rates should be slower than those of the column to its right.
n2, n!, log, n, n log, n, 3n, 5n² +3, 2", 10000, n log3 n, 100n, 3log2n
2. Using the definition of big-O, show 100n + 5 = 0(n). Give a particular c and no.
3. Using the definition of big-O, show that n =
O(2"). Give a particular c and no.
4. Identify a function f(n) which has 3n + 4n2 + 3n!
n = 0(n!) and n² = 0(n!).
O(f (n)). You may use the facts that
Transcribed Image Text:1. Organize the following functions into six columns. Items in the same column should have the same asymptotic growth rates (big-O). If a column is to the left of another column, all its growth rates should be slower than those of the column to its right. n2, n!, log, n, n log, n, 3n, 5n² +3, 2", 10000, n log3 n, 100n, 3log2n 2. Using the definition of big-O, show 100n + 5 = 0(n). Give a particular c and no. 3. Using the definition of big-O, show that n = O(2"). Give a particular c and no. 4. Identify a function f(n) which has 3n + 4n2 + 3n! n = 0(n!) and n² = 0(n!). O(f (n)). You may use the facts that
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