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Math Help - Slant asymptote

  1. #1
    DBA
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    Slant asymptote

    How can I find the slant asymptote of f(x)= x^3 / x^2 +1

    Thanks for any help!
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  2. #2
    Flow Master
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    Quote Originally Posted by DBA View Post
    How can I find the slant asymptote of f(x)= x^3 / x^2 +1

    Thanks for any help!
    Using polynomial long division, \frac{x^3}{x^2 + 1} = x - \frac{x}{x^2 + 1} ....
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    Quote Originally Posted by DBA View Post
    How can I find the slant asymptote of f(x)= x^3 / x^2 +1

    Thanks for any help!

    Provided the respective limits exists, the line y=ax+b is a slant asymptote in the +\infty zone to the function y=f(x), when:

    a=\lim_{x\rightarrow \infty}\frac{f(x)}{x}

    b=\lim_{x\rightarrow \infty}(f(x)-ax)

    Do as above for x\rightarrow -\infty for asymptotes in the -\infty zone.

    You can also find slant asymptotes of rational functions (like yours) by long polynomial division, but the above method works for a larger kind of functions.

    Tonio
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