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Math Help - Slant Asymptote

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    Slant Asymptote

    What is the equation of the slant asymptote for R(x) = x^2 - x + 17 divided by x^2 + 1?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tricey36 View Post
    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
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by tricey36 View Post
    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.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    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
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