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Math Help - evalute this limit

  1. #1
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    evalute this limit

    \lim_{x\rightarrow \infty }\sqrt{x+\sqrt{x}}+\sqrt{x}
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  2. #2
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    Hints:
    Limit of a power = Power of the limit.
    Limit of a sum = Sum of the limit.
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  3. #3
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    i did not get
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  4. #4
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    A square root is the same as taking to the power of \frac{1}{2}.

    So now use the fact that the limit of the power is the same as the power of the limit.
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  5. #5
    MHF Contributor chisigma's Avatar
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    May be that there is a '+' instead of a '-' and the limit is...

    \displaystyle \lim_{x \rightarrow \infty} \sqrt{x + \sqrt{x}} - \sqrt {x} (1)

    In that case is...

    \displaystyle \lim_{x \rightarrow \infty} \sqrt{x + \sqrt{x}} - \sqrt {x}= \lim_{x \rightarrow \infty} \frac{\sqrt{x}}{\sqrt{x + \sqrt{x}} + \sqrt {x}} =

    \displaystyle = \lim_{x \rightarrow \infty} \frac{1}{1 + \sqrt{1 + \frac{1}{\sqrt{x}}}} = \frac{1}{2} (2)

    Kind regards

    \chi \sigma
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