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Math Help - How to prove

  1. #1
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    How to prove

    There is some real number x for which x= cosx
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  2. #2
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    The function f(x)=\cos(x) - x is continuous.
    f(0)=1~\&~f\left(\frac{\pi}{2}\right)=\frac{-\pi}{2}.
    Using the intermediate value theorem what that tell you?
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