(Solved): Restructure Newton's method (Case Study: Approximating Square Roots) by decomposing it into three ...

Restructure Newton's method (Case Study: Approximating Square Roots) by decomposing it into three cooperating functions: newton, limitReached, and improveEstimate . The newton function can use either the recursive strategy of Project 2 or the iterative strategy of the Approximating Square Roots Case Study. The task of testing for the limit is assigned to a function named limitReached, whereas the task of computing a new approximation is assigned to a function named improveEstimate. Each function expects the relevant arguments and returns an appropriate value. An example of the program input and output is shown below: Enter a positive number or enter/return to quit: The program's estimate is 1.4142135623746899 Python's estimate is \\( \\quad 1.4142135623730951 \\) Enter a positive number or enter/return to quit Grading When you have completed your program, click the Submit button to record your score.\r\n\r\nThe program's newton, limitReached, and improvedEstimate functions work as expected. 1 out of 3 checks passed. Review the results below for more details. Checks Unit Test \\( \\bullet \\) Incomplete The newton function returns the square root of ' \\( x \\) ' Unit Test \\( \\bullet \\) Incomplete The limitReached function returns True if the estimate is within the tolerance, if not, False Unit Test \\( \\bullet \\) complete The improveEstimate function returns an improved estimate def newton(number, initial_estimate, max_iterations=1000, tolerance=1e-10): Enter a positive number or press Enter/Re turn to quit: 2 The program's estimate is 1.4142135623746 899 Python's estimate is 1.4142135623730951 Enter a positive number or press Enter/Re turn to quit: quit Traceback (most recent call last): File \"/root/sandbox/newton.py\", line 34 , in 〈module> main() File \"/root/sandbox/newton.py\", line 26 , in main number \\( = \\) float \\( ( \\) input_str) ValueError: could not convert string to \\( f \\) loat: 'quit' \\#Uses the Newton's method formula to improve the present estimate. return \\( 0.5 * \\) (estimate + number / estimate) def main(): \\#Main function for calculating square roots interactively using Newton' while True: input_str = input(\"Enter a positive number or press Enter/Return to if input_str \\( ==\" \" \\) \" break number \\( = \\) float \\( ( \\) input_str) initial_estimate \\( = \\) number \\( / 2 \\) program_estimate \\( = \\) newton (number, initial_estimate) python_estimate \\( = \\) number \\( * * 0.5 \\) print(\"The program's estimate is\", program_estimate) print(\"Python's estimate is\", python_estimate) if _- name__ == \"_-main__\" : \\( \\operatorname{main}() \\)