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Math Help - Higher Limits, L'Hospital's Rule

  1. #1
    Del
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    Higher Limits, L'Hospital's Rule

    I can't figure out how to solve this:

    = ?

    Please help!
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  2. #2
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    You don't need to apply that Rule, just remember that

    \forall\,x\in\mathbb R,\,\lim_{n\to\infty}\left(1+\frac xn\right)^n=e^{x}.

    And,

    \lim_{x \to \infty } \left( {1 + \frac{7}<br />
{x}} \right)^{x/5} = \lim_{x \to \infty } \left[ {\left( {1 + \frac{7}<br />
{x}} \right)^x } \right]^{1/5}
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  3. #3
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    When I solve it, I get [1 + (Infinity / Infinity)]. I don't know what I'm doing wrong.
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