The instructions are on the left, the code is on the right Python only! Instructionsnewton.py1 # Modify the code below2 II I| ||Restructure Newton's method (Case Study: Approximating Square Roots)3 Program: newton.pyby decomposing it into three cooperating functions: newton ,4 Author: KenlimitReached , and improveEstimate.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 rootusing Newton's method of successive approximations, andPython's own estimate using math.sqrt.The newton function can use either the recursive strategy of Project 2 or8.the 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 is11assigned to a function named improveEstimate . Each function expects12 import maththe relevant arguments and returns an appropriate value.1314 # Receive the input number from the user15 x = float(input("Enter a positive number: "))An example of the program input and output is shown below:1617 # Initialize the tolerance and estimate18 tolerance = 0.000001Enter a positive number or enter/return to quit: 219 estimate = 1.020The program's estimate is 1.414213562374689921 # Perform the successive approximationsPython's estimate is1.414213562373095122 while True:Enter a positive number or enter/return to quit23estimate = (estimate + x / estimate) / 224abs(xestimate ** 2)differenceif difference <= tolerance:%3D2526breakGrading2728 # Output the result29 print ("The program's estimate is", estimate)30 print("Python's estimate is', math.sqrt(x))

Program Code: import mathdef limitReached(val,last): return abs(val-last) < 1e-2def…

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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Chapter1: Introduction

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Representation of Polynomial

It is necessary for the polynomial expression that each expression consists of two parts:

Question

The instructions are on the left, the code is on the right

Python only!

Instructions
newton.py
1 # Modify the code below
2 II I| ||
Restructure Newton's method (Case Study: Approximating Square Roots)
3 Program: newton.py
by decomposing it into three cooperating functions: newton ,
4 Author: Ken
limitReached , and improveEstimate.
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.
The newton function can use either the recursive strategy of Project 2 or
8.
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
11
assigned to a function named improveEstimate . Each function expects
12 import math
the relevant arguments and returns an appropriate value.
13
14 # Receive the input number from the user
15 x = float(input("Enter a positive number: "))
An example of the program input and output is shown below:
16
17 # Initialize the tolerance and estimate
18 tolerance = 0.000001
Enter a positive number or enter/return to quit: 2
19 estimate = 1.0
20
The program's estimate is 1.4142135623746899
21 # Perform the successive approximations
Python's estimate is
1.4142135623730951
22 while True:
Enter a positive number or enter/return to quit
23
estimate = (estimate + x / estimate) / 2
24
abs(x
estimate ** 2)
difference
if difference <= tolerance:
%3D
25
26
break
Grading
27
28 # Output the result
29 print ("The program's estimate is", estimate)
30 print("Python's estimate is
', math.sqrt(x))

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