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Find the real root of the equation 3x-cosx-1=0 correct to four decimal places using the Newton Raphson Method.

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  1.  Find a real root of the equation x3 – x – 1 = 0 using Newton - Raphson method, correct to four decimal places.

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  2. let y = 3x - cosx - 1
    y' = 3 + sinx

    newx = oldx - (3oldx - cos(oldx) - 1)/(3 + sin(oldx))
    let's take a look
    http://www.wolframalpha.com/input/?i=plot+y+%3D+3x-cosx-1
    it appears x = .5 could be a good start
    x ..... newx
    .5 ---- .6085..
    .6085 .60710
    .60710 .60710 <---- same result correct to 5 decimals

    check in original:
    LS = 3(.60710) - cos(60710) - 1
    = -.0000058... , not bad

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