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Math Help - Limits

  1. #1
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    Limits

    Need to find the limits of the following

    8x-6/4x^3+6 as x approaches infinity



    square root of x^4+1/x^3+4 as x approaches negative infinity
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  2. #2
    Super Member Aryth's Avatar
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    Quote Originally Posted by elexis10 View Post
    Need to find the limits of the following

    8x-6/4x^3+6 as x approaches infinity



    square root of x^4+1/x^3+4 as x approaches negative infinity
    For the first one, you just simply divide both sides of the fraction by x^3:

    \lim_{x \to \infty} \frac{\frac{1}{x^3}}{\frac{1}{x^3}}\frac{8x - 6}{4x^3 + 6}

    This turns the limit into:

    \lim_{x \to \infty} \frac{\frac{8}{x^2} - \frac{6}{x^3}}{4 + \frac{6}{x^3}}

    Now we use the property that the limit of a quotient is the quotient of the limits:

    \frac{\lim_{x \to \infty} \frac{8}{x^2} - \frac{6}{x^3}}{\lim_{x \to \infty} 4 + \frac{6}{x^3}}

    The numerator goes to 0 and the denominator goes to 4, so that:

    \lim_{x \to \infty} \frac{8x - 6}{4x^3 + 6} = \frac{0}{4} = 0

    As for the second one, it involves multiplication by \frac{\frac{1}{x^2}}{\frac{1}{x^2}}, but it requires a little thought, basically that:

    \sqrt{\frac{1}{x^4}} = \frac{1}{x^2}

    You use that and solve it exactly as I solved the first one and you should get it.
    Last edited by Aryth; April 20th 2010 at 11:10 AM.
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