Page 9 - Calc for the Clueless

Important Note 1

Anytime the degree of the top is less than the degree of the bottom, the limit will be 0. You need not do the
work (unless the teacher demands it). You should know that the limit is 0!!!!!!

Example 11—

If we could talk about a degree of the top, it would be 5/2, or 2½. Since the degree of the bottom is 3, which is
more than the top, the limit is 0!

Example 12—

3
Divide everything by x .

We get

If we now let x go to infinity, we get the limit to be 4/-3 or-4/3.

Important Note 2

If the degree of the top is the same as the degree of the bottom, the limit is the coefficient of the highest power
on the top divided by the coefficient of the highest power on the bottom. Again, you do not actually have to do
the division.

Here are two more limits as x goes to infinity.

Example 13—

We get infinity minus infinity. No good!!! What to do? We rationalize the situation. Seriously, we multiply top
and bottom by the conjugate.

So we get

Example 14, Part A—

Example 14, Part B—