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Math Help - Compute the following limit (Use l'Hopital's rule)

  1. #1
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    Compute the following limit (Use l'Hopital's rule)

    [cos(a/x)]^(x^2) as x tends to infinity, where a > 0.

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  2. #2
    Senior Member
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    L = \lim_{x \to \infty} \left[ \cos \left( \frac{a}{x} \right)  \right]^{x^2}

    \ln L = \lim_{x \to \infty} \ln \left[ \cos \left( \frac{a}{x}  \right)  \right]^{x^2}

    \ln L = \lim_{x \to \infty} x^2 \ln \left[ \cos \left( \frac{a}{x}   \right)  \right]

    \ln L = \lim_{x \to \infty} \frac{\ln \left[ \cos \left( \frac{a}{x}   \right)  \right]}{x^{-2}}

    Now you have \frac{0}{0} so you can apply L'H˘pital's rule.
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