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Math Help - Interesting Limits. #1

  1. #1
    Member Miss's Avatar
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    Interesting Limits. #1

    Without L'Hospital's Rule, evaulate:

    \lim_{x\to\infty} \frac { x \, ln( \, ln(x+1) \, ) } { ln(x) }.
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  2. #2
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    For large x :

     ln( ln(x+1) ) > 1

    so

     x ln( ln(x+1) ) > x

    so

    \frac { x \, ln( \, ln(x+1) \, ) } { ln(x) } > \frac{x}{ln(x)}<br />

    which clearly goes to infinity as x goes to infinity
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