MCS177 Homework 3, Fall 1999
Due: October 8, 1999

In this problem, assume that n is a variable ranging over
the nonnegative integers.
As described on page 81, we say that a function of n is big
theta of n^{2} if there are two positive multiples
of n^{2} that the given function always stays
between, except perhaps for some finite number of exceptions.
For example it might stay between 1/4 n^{2} and
2 n^{2} (as on page 81), or between
5 n^{2} and 9 n^{2}.
Using this definition, decide whether each of the following claims is
true or false, and write a brief justification of your answer in each
case.

n^{3} is big theta of n^{2}

n is big theta of n^{2}

3n^{2} is big theta of n^{2}

Do exercise 4.1 on page 81.
Instructor: Max Hailperin