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Find a real root of the equation cos(x) = 3x − 1 correct to four decimal places by using
method of successive approximation.

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  1. you want f(x) = cosx - 3x + 1 = 0
    f(0) = 2
    f(1) = cos(1) - 2 = -1.46
    so f=0 somewhere on (0,1)
    Now, using bisection,
    f(1/2) = 0.377, so f=0 in (0.5,1)
    f(0.75) = -0.51, so f=0 in (0.5,0.75)
    repeat until you get 4 decimal places. x = 0.6071

    If you have calculus, Newton's Method will converge much faster.

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  2. Find the real root of the four decimal x=3x-1

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