Unit 24 Exercises
1. Show that (x² + 2x + 3) / (x + 1) is O(x).
2. Show that 5x4 + x² + 1 is O(x4/2) and x4/2 is O(5x4 + x² + 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) (n² + 3n + 8)(n + 1)
b) (3logn + 5n²)(n³ + 3n + 2)