8. The 'divide and average' method, an old-time method for approximating the square root of any...

                           

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8. The 'divide and average' method, an old-time method for approximating the square root of any positive number a, can be formulated as Xi+1 X;+ X 2 (a) Prove that this is equivalent to the Newton-Raphson algorithm. (b) Implement the method in python and determine the square root of x=2. (c) For Itol-106 ( r tol converge rate (order). x; i+1 - ) determine the number of steps and the X+1 8. The 'divide and average' method, an old-time method for approximating the square root of any positive number a, can be formulated as Xi+1 X;+ X 2 (a) Prove that this is equivalent to the Newton-Raphson algorithm. (b) Implement the method in python and determine the square root of x=2. (c) For Itol-106 ( r tol converge rate (order). x; i+1 - ) determine the number of steps and the X+1