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Math Help - Use IVT to show that cosx=x has at least one x-int.

  1. #1
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    Use IVT to show that cosx=x has at least one x-int.

    I'm having a hard time thinking of a way to solve this problem. How could I start?

    Use the intermediate Value theorem to show that the equation cosx=x has at leat one solution.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    The IVT says simply if f(x) is continuous on a closed interval [a,b] then
    f(x) takes on every value between f(a) and f(b) at least once.


    f(x) =cos(x) - x

    f(0) = 1 > 0

    f(pi) = -1-pi < 0

    Therfore f(x) =cos(x) - x has a zero 0n [0,pi]

    i.e there is an x st cos(x)- x = 0

    or cos(x) = x
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