Page 8 - Calc for the Clueless
P. 8
There are two ways to do this problem. We can rationalize the numerator, remembering not to multiply out the
bottom, or we can factor the bottom into the difference of two squares in a kind of weird way not found in most
algebra books today.
METHOD A
If we now take
METHOD B
which gives the same result.
Example 9—
We will multiply top and bottom by x.
Taking
Limits as x Goes to Infinity
Although this topic occurs later in your book (and my book), some texts talk about limits at infinity very early
on. So I've decided to add this section. If you don't need it now, skip it until later.
We need to know one fact from elementary algebra. The degree of a polynomial in one unknown is the highest
exponent.
Example 10—
3
Divide every term, top and bottom, by x , x to the higher degree.
If we now take the limit as x goes to infinity, every term goes to 0 except the 5 and we get (0 + 0)/(5 + 0) = 0.
