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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 program input and output is shown below: Enter a positive number or

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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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

# 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))
Transcribed Image Text:# 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))
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