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Math Help - Limit to infinity

  1. #1
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    Limit to infinity

    \lim_{x \to \infty} \frac{\sqrt{9x^6 - x}}{x^3 + 1}\\<br />
\frac{\sqrt{9x^6 - x}}{x^3 + 1} \cdot \frac{\frac{1}{x^3}}{\frac{1}{x^3}} = \\<br />
\frac{\frac{\sqrt{9x^6 - x}}{x^3}}{1 + \frac{1}{x^3}} = \\<br />
\frac{(1 + \frac{1}{x^3})(\sqrt{9x^6 - x})}{x^3} = \\<br />
\frac{(1 + \frac{1}{x^3})(\sqrt{9x^6 - x})}{x^3} \cdot \frac{\frac{1}{x^3}}{\frac{1}{x^3}} = \\<br />
\frac{(1 + \frac{1}{x^3})(\sqrt{9x^6 - x})}{x^3}

    And it just repeats over and over again and I can't find anything to divide by without destroying the work I've already done. What am I supposed to do in a loop and there's nothing to divide by?
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  2. #2
    Senior Member
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    Re: Limit to infinity

    Take your denominator into the square root \sqrt{\frac{9x^6-x}{(x^3+1)^2}}.

    You may see that the numerator and denominator both have 6 as their highest power of x.

    Divide top and bottom by x^6.
    Thanks from PhizKid
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