1. ## Slant Asymptote

What is the equation of the slant asymptote for R(x) = x^2 - x + 17 divided by x^2 + 1?

2. Originally Posted by tricey36
What is the equation of the slant asymptote for R(x) = x^2 - x + 17 divided by x^2 + 1?
No wonder you are having problems; this doesn't have a slant asymptote. It has a horizontal asymptote.

$\frac{x^2 - x + 17}{x^2 + 1} = 1 - \frac{x - 16}{x^2 + 1}$

If this had a slant asymptote there would be a term linear in x here.

-Dan

3. Originally Posted by tricey36
What is the equation of the slant asymptote for R(x) = x^2 - x + 17 divided by x^2 + 1?
Did you divide them yet?

The slant asymptote for $\frac{f(x)}{g(x)}$

Is after you divide them through polynomial long divison you should get

$f(x)+\frac{r(x)}{g(x)}$

where $r(x)$ is the remainder. And your slant asymptote is $r(x)$.

So polynomial long divide them and then report back.

4. Originally Posted by Mathstud28
$f(x)+\frac{r(x)}{g(x)}$

where $r(x)$ is the remainder. And your slant asymptote is $r(x)$.
With the additional comment that r(x) must be linear. A construction like this is typically simply called a limit if r(x) contains terms of higher degree than 1. (At least, I've never heard of a "quadratic asymptote.")

-Dan