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Math Help - Evaluating limits at infinity

  1. #1
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    Evaluating limits at infinity


    http://i754.photobucket.com/albums/x...at111757AM.png

    I need help with the 2nd part of the question, evaluating the limit at neg infinity.

    I'm dividing the numerator by the highest power in the denominator (dividing everything by x^3 and x^6 under the radical) and I'm coming up with...

    Lim x-> -oo f(x) = 3+6(1/x^3) / [3 + sqrt((36 + 4(1/x^6))]

    1/x^3 approaches 0 as x approaches neg infinity and 1/x^6 approaches zero as x approaches infinity. leaving me with...

    3 / [(3+sqrt(36)] =3 / (3+3) = 1/3.

    The correct answer is -1. Where did I go wrong?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Evaluating limits at infinity

    Quote Originally Posted by Johnny Walker Black View Post
    The correct answer is -1. Where did I go wrong?
    If x<0 then, x^3<0 so,

    \frac{\sqrt{36x^6+4}}{x^3}=-\frac{\sqrt{36x^6+4}}{|x|^3}=-\sqrt{\frac{36x^6}{|x|^6}+\frac{4}{|x|^6}}=-\sqrt{36+\frac{4}{|x|^6}}\to -6 as x\to -\infty

    Hence, the asked limit is -1 .
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