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calculus

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Determine if the graph of the rational function has a slant asymptote. If it does, find the equation of the slant asymptote.


(2x^3+18x^2+47x+24)/(x^2+6x+5)

  • calculus -

    As x gets very large in magnitude this looks like
    2 x^3/x^2
    or in other words 2x
    line with slope of 2
    y = 2x

  • calculus -

    Oh, when x = 0
    y = 24/5
    so
    y = 2 x + 24/5

  • calculus -

    So a long division to get

    (2x^3 + 18x^2 + 47x + 24)/ (x^2 + 6x + 5) = 2x + 6 + (x-6)/(x^2+6x+5)

    so as x get larger, (x-6)/(x^2+6x+5)
    ---> 0
    and we are left with
    y = 2x + 6

    So the slant asymptote is y = 2x + 6

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