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Math Help - Help me in derivation of limit

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    Help me in derivation of limit

    in limits for 1^∞ type of indeterminate form, the direct solution is e^{g(x)[f(x)-1]}
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    Re: Help me in derivation of limit

    Quote Originally Posted by satyam View Post
    in limits for 1^∞ type of indeterminate form, the direct solution is e^{g(x)[f(x)-1]}
    I am not sure what you mean by "direct solution" but you can convert the form so L'hosiptials rule can be used.

    If \lim_{x \to \infty} f(x)=1 and \lim_{x \to \infty} g(x)=\infty then

    [f(x)]^{g(x)} = \exp [g(x) \ln(f(x))]= \exp \left[ \dfrac{\ln(f(x))}{\frac{1}{g(x)}}\right]

    This is now in the form  \dfrac{0}{0} so you can apply L.H.

    Note the fraction could also be arrainged to get infinity over infinity
    Thanks from satyam
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