Question

Consider the function g (x) = 12x + 4 - cos x. Given g (x) =...

Consider the function g (x) = 12x + 4 - cos x. Given g (x) = 0 has a unique solution x = b in the interval (−1/2, 0), and you can use this without justification.
(a) Show that Newton's method of starting point x0 = 0 gives a number sequence with b <··· <xn+1 <xn <··· <x1 <x0 = 0
(The word "curvature" should be included in the argument!)
(b) Calculate x1 and x2. Use theorem 2 in section 4.2 (page 229- Error bounds for Newtons Method) or intermediate value theorem to show that
x2 - b <0.0000003.
(c) Find a suitable function that you can perform fix piont iteration to find b. Calculate and compare the results of calculating the first three iterations of Newton's method and fix point iteration

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