IS3073 PYTHON PLEASE POST THE ANSWER WITH THE CODE AND THE OUTPUT 1. Package New

Question

IS3073 PYTHON PLEASE POST THE ANSWER WITH THE CODE AND THE OUTPUT

1. Package Newton’s 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 Newton’s 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.)

4. Restructure Newton’s 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.

CASE STUDY: Approximating Square Roots Users of pocket calculators or Python's math module do not have to think about how to compute square roots, but the people who built those calculators or wrote the code for that module certainly did. In this case study, we open the hood and see how this might be done. Request Write a program that computes square roots.

Explanation / Answer

import math

def newton(x, estimate):

    if abs (x-estimate ** 2) <= 0.000001:

            return estimate

    else:

        estimate = newton(x, (estimate + x/estimate)) /2

    return estimate                     

def main():

    while True:

        x = float(input('Enter a positive number or enter/return key to quit: '))

        if x == "":   

                break

        print("Newtons estimate of the sqaure root of ", x, "is: ", newton(x,estimate))

        print("The True value of the square root is: ", math.sqrt(x))

main()

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