LIMITS OF INFINITY: A lot of times a situation will arise that will be unbounded and have no limit. What this means is that no matter what value x takes on y does not change. The point here is that as time goes on, or as the t value increases, the limit approaches the original value and stays there. There is a useful tool on page 648 that allows us to take the limits of infinity.

The for any constant k and n > 0.

In order to make use of this rule you must divide the numerator and denominator by the highest power of x.

EXAMPLE:

In this case, the limits of the numerator and denominator do not exist. If we divide the numerator and denominator by the highest power of x, we get the following:

Remember the are all zero by definition.

ANY QUESTIONS?

This idea of limits of infinity comes in use when you are dealing with cost benefit analysis as the next example shows.

The percentage "p" of pollution that can be removed from the smoke stacks of an industrial plant by spending C dollars is given by

.

Find the percentage of the pollution that could be removed if spending C was allowed to increase without bound. Can 100% of the pollution be removed?

SOLUTION:

Since it was stated that spending C was allowed to increase without bound, this means infinity we have the following

= =

This means that the percentage remains at 100%, so no, 100% c

can’t be removed.

HOMEWORK pg 652 (31,33,36, and 37) solve them only do not graph