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
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
Enter a positive number or enter/return to quit: 2 The program's estimate is 1.4142135623746899 Python's estimate is 1.4142135623730951 Enter a positive number or enter/return
![# Modify the code below
Program: newton.py
Author: Ken
Compute the square root of a number.
1. The input is a number.
2. The outputs are the program's estimate of the square root
using Newton's method of successive approximations, and
Python's own estimate using math.sqrt.
import math
# Receive the input number from the user
float (input("Enter a positive number: "))
X =
# Initialize the tolerance and estimate
tolerance = 0.000001
estimate = 1.0
# Perform the successive approximations
while True:
estimate = (estimate + x / estimate) / 2
difference = abs(x
estimate ** 2)
if difference <= tolerance:
break
# Output the result
print("The program's estimate is", estimate)
print("Python's estimate is
", math.sqrt(x))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1580620b-ec3d-48da-8d5f-e0e1d6dd1757%2F0caee699-9a7a-4f8e-a8ff-3988a0608c80%2Fray6jt_processed.png&w=3840&q=75)
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