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Math Help - Limit help, radical in the numerator!!! (Answer provided but idk how it comes about)

  1. #1
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    Limit help, radical in the numerator!!! (Answer provided but idk how it comes about)

    the problem is

    the lim as x approaches inifinity of

    √(9x^6 - 1)/(x^3 - 1)

    Correct Answer: 3


    the 1's are constants being subtracted, not being subtracted from the exponents themselves.

    I tried mulitplying both by 9x^6-1 but it just wasn't a good time and I couldn't see it ever working out.

    I tired multiplying by 1/x but that wasn't really a tea party either. I'm really at a loss of what to do but I figure i'll end up with 3 in the num. and 1 in the denom since the final answer is 3.
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    Re: Limit help, radical in the numerator!!! (Answer provided but idk how it comes abo

    Quote Originally Posted by skinsdomination09 View Post
    the problem is

    the lim as x approaches inifinity of

    √(9x^6 - 1)/(x^3 - 1)

    Correct Answer: 3
    \frac{{\sqrt {9{x^6} - 1} }}{{{x^3} - 1}} = \frac{{\sqrt {9 - \dfrac{1}{{{x^6}}}} }}{{1 - \dfrac{1}{{{x^3}}}}}
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    Re: Limit help, radical in the numerator!!! (Answer provided but idk how it comes abo

    Quote Originally Posted by Plato View Post
    \frac{{\sqrt {9{x^6} - 1} }}{{{x^3} - 1}} = \frac{{\sqrt {9 - \dfrac{1}{{{x^6}}}} }}{{1 - \dfrac{1}{{{x^3}}}}}
    I'm sorry I gotta be honest I really don't see what you did there. did you multiply by 1/x^6 or divide by x
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  4. #4
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    Re: Limit help, radical in the numerator!!! (Answer provided but idk how it comes abo

    Quote Originally Posted by skinsdomination09 View Post
    I'm sorry I gotta be honest I really don't see what you did there. did you multiply by 1/x^6 or divide by x
    divide numerator and denominator by x^3
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