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Math Help - Limit and inverse function

  1. #1
    Junior Member
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    Post Limit and inverse function

    I have two questions:-

    simplify the expression
    cos(tan inverse(x))

    evaluate the limit
    lim(as x>infinty) (xe^(1/x)-x)
    Last edited by Krizalid; February 4th 2009 at 05:53 AM.
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  2. #2
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    Quote Originally Posted by Sally_Math View Post
    evaluate the limit
    lim(as x>infinty) (xe^(1/x)-x)
    <br />
\lim_{x\to\infty}{x e^{\frac{1}{x}}-x}=\lim_{x \to \infty}{x(e^{\frac{1}{x}}-1)} = \lim_{x \to \infty}{\frac{e^{\frac{1}{x}}-1}{\frac{1}{x}}}

    Now you can apply L'Hospital's rule  \lim_{x \to \infty}{\frac{(e^{\frac{1}{x}}-1)'}{(\frac{1}{x})'}} = \lim_{x \to \infty}{e^{\frac{1}{x}}} = 1
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