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Math Help - Limit Problem

  1. #1
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    Limit Problem

    Please help with this problem i have final tomorrow

    Limit Problem-codecogseqn-1-.gif
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  2. #2
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    Re: Limit Problem

    Seems to tend to infinity, no?
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  3. #3
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    Re: Limit Problem

    Quote Originally Posted by Telo View Post
    Please help with this problem i have final tomorrow

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    \displaystyle \begin{align*} \sqrt{n^2 + 3} + \sqrt{n^2 + 8} &> \sqrt{n^2} + \sqrt{n^2} \\ &= |n| + |n| \\ &= 2|n| \end{align*}

    Since \displaystyle \begin{align*} 2|n| \to \infty \end{align*}, therefore so must \displaystyle \begin{align*} \sqrt{n^2 + 3} + \sqrt{n^2+8} \end{align*}.
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  4. #4
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    Re: Limit Problem

    Quote Originally Posted by Telo View Post
    Please help with this problem i have final tomorrow

    Click image for larger version. 

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    Quite frankly this is a trivial problem. As the others have said, as n goes to infinity, both parts do also and so their sum does.

    A much more interesting problem would be \lim_{x\to\infty}\left[\sqrt{n^2+ 3}- \sqrt{n^2+ 8}\right]. For that, I would recommend multiplying by the "unit fraction" \frac{\sqrt{n^2+ 3}+ \sqrt{n^2+ 8}}{\sqrt{n^2+3}+ \sqrt{n^2+ 8}}.
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  5. #5
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    Re: Limit Problem

    Quote Originally Posted by Telo View Post
    Please help with this problem i have final tomorrow
    You have a final the day after Christmas?
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