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Math Help - iterative formula

  1. #1
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    iterative formula

    a) given that A is the root of the equation

    arccos(x-1)= square root of x+2

    show that 0<A<1

    b) use the iterative formula

    x(n+1) = 1+cos of the square root of xn +2

    sorry, the n+1 and n are supposed to be subscript.

    when i tried to do part b, i got 1.998....which is not between 0 and 1 so i must be doing it wrong!

    can anyone help?
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  2. #2
    Member Henderson's Avatar
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    Check to make sure you're using radians. It sounds like you're in degrees.
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  3. #3
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    you're right! how stupid of me. thanks!
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Oranges&Lemons View Post
    a) given that A is the root of the equation

    arccos(x-1)= square root of x+2

    show that 0<A<1
    note that the function f(x) = \arccos (x - 1) - \sqrt{x + 2} is continuous on [0,1]

    now f(0) > 0 and f(1) < 0. thus by the intermediate value theorem, there is some x \in (0,1) such that f(x) = 0. this x is a root. we choose A to be this x

    b) use the iterative formula

    x(n+1) = 1+cos of the square root of xn +2

    sorry, the n+1 and n are supposed to be subscript.
    use the iterative formula to do what? show that 0 < A < 1?
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