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Math Help - Limits

  1. #1
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    Limits

    I'm having trouble with these limits. Any help would be appreciated.

    \lim_{x\to +\infty}\frac{\sqrt[3]{{x}^{5}-3x}}{{x}^{2}+4}

    \lim_{x\to 0^{+}} \sqrt{\frac{x+1}{x}}
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Alvy View Post
    I'm having trouble with these limits. Any help would be appreciated.

    \lim_{x\to +\infty}\frac{\sqrt[3]{{x}^{5}-3x}}{{x}^{2}+4}

    \lim_{x\to 0^{+}} \sqrt{\frac{x+1}{x}}
    Observe:

    \frac{\sqrt[3]{{x}^{5}-3x}}{{x}^{2}+4}=\frac{x^{5/3}(1-3/x^4)}{x^2(1+4/x^2)}=\frac{(1-3/x^4)}{x^{1/3}(1+4/x^2)}

    Now you should be able to determine the limit.

    CB
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Alvy View Post
    I'm having trouble with these limits. Any help would be appreciated.

    \lim_{x\to +\infty}\frac{\sqrt[3]{{x}^{5}-3x}}{{x}^{2}+4}

    \lim_{x\to 0^{+}} \sqrt{\frac{x+1}{x}}
    For the second one:

     \sqrt{\frac{x+1}{x}} = \sqrt{\frac{\frac{x+1}{x}}{\frac{x}{x}}} = \sqrt{\frac{1+{\frac{1}{x}}}{1}}= \sqrt {1+{\frac{1}{x}}}
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  4. #4
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    Thank you very much.
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