in python 3.2

1. Package Newtons method for approximating square roots (Case Study 3.6) in a function named newton. This function expects the input number as an argument and returns the estimate of its square root. The script should also include a main function that allows the user to compute square roots of inputs until she presses the enter/return key.

2. Convert Newtons method for approximating square roots in Project 1 to a recursive function named newton. (Hint: The estimate of the square root should be passed as a second argument to the function.)

3. Restructure Newtons method (Case Study 3.6) by decomposing it into three cooperating functions. The newton function can use either the recursive strategy of Project 1 or the iterative strategy of Case Study 3.6. 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.