# horizontal asymptotes

• Jul 17th 2008, 04:19 AM
robasc
horizontal asymptotes
I am helping a friend and I am trying to remember if this is the correct way to figure out this horizontal asymptote?

equation:

1.493x^2 - 39.06x + 273.5
D = ---------------------------
0.0051x^2 - 0.1398x + 1

1.493
------- = 292.745098
0.0051

y = 292.745098 horizontal asymptote

is this correct?
• Jul 17th 2008, 04:20 AM
mr fantastic
Quote:

Originally Posted by robasc
I am helping a friend and I am trying to remember if this is the correct way to figure out this horizontal asymptote?

equation:

1.493x^2 - 39.06x + 273.5
D = ---------------------------
0.0051x^2 - 0.1398x + 1

1.493
------- = 292.745098
0.0051

y = 292.745098 horizontal asymptote

is this correct?

Yes.
• Jul 17th 2008, 05:21 AM
Chop Suey
Yes, your way is correct. To understand why/how, take the limit of your rational function as x goes to infinity.

$\displaystyle f(x) = \frac{1.493x^2 - 39.06x + 273.5}{0.0051x^2 - 0.1398x + 1}$

$\displaystyle \lim_{x \to \pm \infty} \frac{1.493x^2 - 39.06x + 273.5}{0.0051x^2 - 0.1398x + 1}$

$\displaystyle = \lim_{x \to \pm \infty} \frac{1.493x^2}{0.0051x^2}$

$\displaystyle = \frac{1.493}{0.0051} = 292.745098$
• Jul 17th 2008, 06:08 AM
robasc
one more question
This question is is states that

D is national defense outlays in billions of dollars ranging from 7 to 15
where 7 = 1997.

Determine the horizontal asymptote of the graph of the model. What does it represent in the context of the situation.

Ok, I know what the horizontal asymptote is and I believe it means that from 1998 to 2005 there is a rise in defense outlays, is this correct?