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Math Help - L'Hospital Rule Indeterminate INF-INF

  1. #16
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    Quote Originally Posted by Krizalid View Post
    Just in case, here's a beauty limit if you wanna practice
    I know where you get that problem from. It was from the Putnam. (I have a Calculus book which has Putnam problems in it and I remember I did this one).

    The one they have is actually stronger version.
    Let a!=0 and a>0.

    ---
    I do not know why this call this "beauty limit". If the limit was something like pi^a, then that would be a beauty limit.
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  2. #17
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    Quote Originally Posted by The Great One
    It is simple with L'Hopital try to find without it.
    I recommend to use the following inequality,

    a^x-a^{x-1} <= a^x - 1 <= a^x

    Thus,

    (a^x-a^{x-1})^{1/x} <= (a^x - 1)^{1/x} <= a

    Right? I did not check this yet and about to sleep.
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