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Math Help - Limits

  1. #1
    Junior Member
    Joined
    Aug 2009
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    Limits

    Hi eveybody,

    I find some difiiculties to calculate the following limits:

    1)- \lim_{x\to 1} (2-3x+x^2)tan(\frac{\pi}{2}x)

    2)- \lim_{x\to \frac{\pi}{4}} \frac{sinx-cosx}{x+xcos4x}


    Can you help me please?

    And thank's anyway
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    1) \lim_{x\to 1}(2-3x+x^2)\tan\frac{\pi x}{2}=\lim_{x\to 1}\frac{(x-1)(x-2)}{\cos\frac{\pi x}{2}}\cdot\sin\frac{\pi x}{2}=

    =\lim_{x\to 1}\frac{(x-1)(x-2)}{\sin\left(\frac{\pi}{2}-\frac{\pi x}{2}\right)}\cdot\sin\frac{\pi x}{2}=

    =-\lim_{x\to 1}\frac{1-x}{\sin\frac{\pi(1-x)}{2}}\cdot\lim_{x\to 1}(x-2)\sin\frac{\pi x}{2}=-\frac{2}{\pi}\cdot(-1)=\frac{2}{\pi}
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