# Thread: Find an equation of the horizontal asymptote

1. ## Find an equation of the horizontal asymptote

Hey guys, forgot how to do this. All I remember is that the problem is given in factor form and product form and you have to choose the easier one to work with, but I'm totally drawing a blank on what to do. I know that a horizontal asymptote will be of the form y = x, but thats about it. Any help much appreciated.

Let R(x) = (4x^2)(2x - 1)/7(5x + 3)(x + 2)^2 = (8x^3 - 4x^2)/(35x^2 - 119X^2 + 56x + 84)

Find an equation of the horizontal asymptote of R(x).

2. Originally Posted by leviathanwave
Hey guys, forgot how to do this. All I remember is that the problem is given in factor form and product form and you have to choose the easier one to work with, but I'm totally drawing a blank on what to do. I know that a horizontal asymptote will be of the form y = x, but thats about it. Any help much appreciated.

Let R(x) = (4x^2)(2x - 1)/7(5x + 3)(x + 2)^2 = (8x^3 - 4x^2)/(35x^2 - 119X^2 + 56x + 84)

Find an equation of the horizontal asymptote of R(x).
There is none.

The horizontal asymptote is determined by the degree in the numerator and denominator, and (in case you forgot) the degree of a polynomial is the highest exponent of that polynomial.

In this problem, the degree of the numerator is 3 (from 8x^3) and in degree of the denominator is 2 (from 35x^2). Since the degree in the numerator is greater than the degree of the denominator, we don't get a horizontal asymptote. [NOTE: the only time we get a horizontal asymptote is when the degrees are the same or if the degree of the denominator is greater.]

In this case, all we get is a slant asymptote. To find out what that asymptote is, use polynomial division. (If you have never heard of a "slant asymptote" or "polynomial division" then forget I mentioned this and just know there is no horizontal asymptote.)

3. Hello, leviathanwave!

There seems to be typos in the problem . . .

R(x) .= .[4x²(2x - 1)] / [7(5x - 3)(x + 2)²] .= .(8x³ - 4x²)/(35x³ - 119x² + 56x - 84)

Find an equation of the horizontal asymptote of R(x).
For a horizontal asymptote, take the limit of R(x) as x→∞

Divide top and bottom by x³ and take the limit:

. . . . . . . . . . . 8 - 4/x . . . . . . . . . . . 8
. lim .-------------------------------- . = . ---
x→∞ .35 - 119/x + 56/x² - 84/x³ . . . .35

Therefore, the horizontal asymptote is: .y .= .8/35