Page 42 - Calc for the Clueless

Definition A

Degree—if a polynomial has one variable, it is the highest exponent.

Definition B

Leading coefficient—the coefficient of the highest power.

Example 7—

Degree is 6. Leading coefficient is -7.

Horizontal Asymptote Type I

(Don't be scared. There are only two types!)

Suppose y = P(x)/Q(x). P and Q are polynomials. If the degree of P (top) is less than the degree of Q (bottom),
the horizontal asymptote is y = 0, the x axis.

Example 8—

3
4
As x goes to infinity 3/X , -7/X , and 8/x all go to 0. So y = (0 - 0)/(0 + 5) = 0. The asymptote is y = 0!!!
2
Note I
4
We divided by x , that is, x to the highest power.

Note 2

When you do the problem, don't actually do this. Since you know anytime the degree of the top is smaller than
the degree of the bottom you get y = 0, just use y = 0 when this happens. Easy, isn't it?!!

Horizontal Asymptote Type 2

Example 9—

Both degrees are 3. If the degree of the top equals the degree of the bottom, the horizontal asymptote is y = a/b,
where a is the leading coefficient of the top and b is the leading coefficient of the bottom. Asymptote is y = 6/(-
7). Let us verify.

As x goes to infinity, 2/x and 5/x go to 0. Asymptote is y =-6/7.
2
3