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Math Help - hard limit problem involving a trig. exponent

  1. #1
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    hard limit problem involving a trig. exponent

    PROBLEM:


    \lim_{x\to\(\pi^+)}{(1+3sinx)^{cot(x)}}


    ATTEMPT:

    Does L'Hopital's Rule apply work for this problem? I don't think so, because it is not in the appropriate indeterminate form; for, it would be 1^\infty. But I don't know any elementary methods that would be appropriate here, nor any limit properties. :/
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: hard limit problem involving a trig. exponent

    Yes, L'Hospital's works. Try this - take the log of the expression, and you get:

    \lim ( \ln (1+3 \sinx)^{cotx}))= \lim ( \frac { \cos x \ln (1+3\sin x)}{\sin x})

    Now use L'Hospital's, and you shoud find that this limit approahes a value, let's call it A. The the limit of the original problem is  e^A.
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