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Math Help - root limit question..

  1. #1
    MHF Contributor
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    1,401

    root limit question..

    [imath]
    \lim _{x->+\infty} \frac{(x-\sqrt{x^2-1})^n+(x+\sqrt{x^2-1})^n}{x^n}=\lim _{x->+\infty} \frac{(1-\sqrt{x-\frac{1}{x}})^n+(1+\sqrt{x-\frac{1}{x}})^n}{1}=\infty-\infty
    [/imath]

    this is as far as i can go
    i got undefined form

    ??
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  2. #2
    Member arpitagarwal82's Avatar
    Joined
    Feb 2009
    Posts
    103
    There is an error.
    when x goes inside square root, it becomes x^2.
    So correct is

    \lim _{x->+\infty} \frac{(1-\sqrt{1-\frac{1}{x^2}})^n+(1+\sqrt{1-\frac{1}{x^2}})^n}{1}

    Now proceed.
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