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Math Help - More Proofs

  1. #1
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    More Proofs

    Let \alpha > 0. Prove that no matter how small \alpha is, there is an N \epsilon R such that ln x \leq x^{\alpha} for all x \leq N. Note: N depends on \alpha.

    I need to use the mean value theorem to do this.
    I started by finding the difference of the derivatives of both functions.
    Then didnt know where to go... Any help would be greatly appreciated...
    Last edited by Caity; November 21st 2008 at 09:55 AM.
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  2. #2
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    Fixed Latex error... sorry about that
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  3. #3
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    I've been playing around with this problem... This is what I have so far...

    g' (x) - f' (x) is decreasing when \alpha is very small.

    For \alpha = \frac{1}{200} or smaller x = 2.27

    The inequality only holds true for x\leq 2.27 and I need to find a N\leq x

    Can anyone help me with explaining this or let me know if I am doing something wrong please??
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