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Math Help - Limit Question

  1. #1
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    Limit Question

    Given that \Biggl| \cos^{-1} \biggl( \frac{1}{n} \biggr) \Biggr|< \frac{\pi}{2} evaluate:

    \lim_{n \to \infty} \frac{2}{\pi} (n+1) \cos^{-1} \biggl(\frac{1}{n} \biggr) -n
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  2. #2
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    Quote Originally Posted by Chandru1 View Post
    Given that \Biggl| \cos^{-1} \biggl( \frac{1}{n} \biggr) \Biggr|< \frac{\pi}{2} evaluate:

    \lim_{n \to \infty} \frac{2}{\pi} (n+1) \cos^{-1} \biggl(\frac{1}{n} \biggr) -n
    put n=\sec t. then you'll have a simple limit \lim_{t \to\frac{\pi}{2}}\frac{2t(1+\cos t) - \pi}{\pi \cos t}=1-\frac{2}{\pi}, by applying L'Hopital once.
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