Unit 24 Exercises

1. Show that (x + 2x + 3) / (x + 1)  is O(x).

2. Show that  5x4 + x + 1  is  O(x4/2)  and  x4/2  is  O(5x4 + x + 1).

3. Show that  2n  is  O(3n)  but that  3n is  not  O(2n).

4. Explain what it means for a function to be O(1).

5. Give as good (i.e. small) a big-O estimate as possible for each of the following functions.

    a) (n + 3n + 8)(n + 1)

    b) (3logn + 5n)(n + 3n + 2)

 

Answer for these exercises