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fixed_point - MAT 2384-Practice Problems on xed-point...

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MAT 2384-Practice Problems on fixed-point iteration, Newton’s Methods and Secant method 1. Apply fixed-point iteration to find the root of sin x - x 1 . 4 = 0 in the interval 1 , π 2 to 4 decimal places. Use x 0 = 1 . 4 and make sure that the conditions for convergence of the iteration sequence are satisfied. 2. Apply fixed-point iteration to find the root of x 4 - x + 0 . 2 = 0 near x = 0 to 5 decimal places. Use x 0 = 0. 3. Apply fixed-point iteration to find the smallest positive solution of sin x = e - 0 . 5 x in the interval [0 . 1 , 1] to 5 decimal places. Use x 0 = 1 and make sure that the conditions for convergence of
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