The question and code are both attatched as images. Please only modify the already existing code to do what the question asked it. Python Thanks! 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 orthe iterative strategy of the Approximating Square Roots Case Study. Thetask of testing for the limit is assigned to a function namedlimitReached , whereas the task of computing a new approximation isassigned to a function named improveEstimate . Each function expectsthe 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: 2The program's estimate is 1.4142135623746899Python's estimate is1.4142135623730951Enter a positive number or enter/return to quit 1 # Modify the code below3 Program: newton.py4 Author: Ken5 Compute the square root of a number.6 1. The input is a number.7 2. The outputs are the program's estimate of the square rootusing Newton's method of successive approximations, andPython's own estimate using math.sqrt.8.1112 import math1314 # Receive the input number from the userfloat(input("Enter a positive number: "))|15 x =1617 # Initialize the tolerance and estimate18 tolerance = 0.00000119 estimate = 1.02021 # Perform the successive approximations22 while True:estimate = (estimate + x / estimate) / 2difference = abs(x - estimate ** 2)if difference <= tolerance:break232425262728 # Output the result29 print("The program's estimate is", estimate)30 print("Python's estimate is', math.sqrt(x))31

import math # intialize the tolerance# set _estimate to default value as 1def…

Answered: Restructure Newton's method (Case…

Restructure Newton's method (Case Study: Approximating Square Roots) by decomposing it into three cooperating functions: newton , limitReached , and improveEstimate.

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Question

The question and code are both attatched as images.

Please only modify the already existing code to do what the question asked it.

Python

Thanks!

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: 2
The program's estimate is 1.4142135623746899
Python's estimate is
1.4142135623730951
Enter a positive number or enter/return to quit

1 # Modify the code below
3 Program: newton.py
4 Author: Ken
5 Compute the square root of a number.
6 1. The input is a number.
7 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.
8.
11
12 import math
13
14 # Receive the input number from the user
float(input("Enter a positive number: "))
|15 x =
16
17 # Initialize the tolerance and estimate
18 tolerance = 0.000001
19 estimate = 1.0
20
21 # Perform the successive approximations
22 while True:
estimate = (estimate + x / estimate) / 2
difference = abs(x - estimate ** 2)
if difference <= tolerance:
break
23
24
25
26
27
28 # Output the result
29 print("The program's estimate is", estimate)
30 print("Python's estimate is
', math.sqrt(x))
31

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