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Math Help - Confusing Answers

  1. #1
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    Confusing Answers

    \lim x \rightarrow \infty

    (e^{x} + x)^{\dfrac{9}{x}}

    (e^{\infty} + \infty)^{\dfrac{9}{\infty}}

    \infty^{0}
    - Indeterminate
    OR

    \lim x \rightarrow \infty

    x^{\dfrac{4}{x}}

    \infty^{\dfrac{4}{\infty}}

    \infty^{0}
    = 1

    Both problems involve infinity to the 0 power. But they come out differently. Why?
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  2. #2
    MHF Contributor
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    Re: Confusing Answers

    Hey Jason76.

    Basically the things inside the parentheses grow at different rates in relation to 9/x as x -> infinity.

    I'd suggest you look at how the exponential function is defined in terms of limits and compare that with your x^(0) as x -> infinity as this will give you a better way of answering your own question.
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