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Instructions newton.py + 1 # Modify the code below Restructure Newton's method (Case Study: Approximating 3 Program: newton.py Square Roots) by decomposing it into three cooperating 4 Author: Ken functions: newton , 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 using Newton's method of successive approximations, a The newton function can use either the recursive strategy of Project 2 or the iterative strategy of the Approximating Square Python's own estimate using math.sqrt. Roots Case Study. The task of testing for the limit is assigned to a function named limitReached , whereas the task of computing 11 a new approximation is assigned to a function named 12 import math improveEstimate. Each function expects the relevant |13 14 # Receive the input number from the user |15 x = float(input("Enter a positive number: ")) arguments and returns an appropriate value. 16 An example of the program input and output is shown below: 17 # Initialize the tolerance and estimate 18 tolerance = 0.000001

Instructions newton.py + 1 # Modify the code below Restructure Newton's method (Case Study: Approximating 3 Program: newton.py Square Roots) by decomposing it into three cooperating 4 Author: Ken functions: newton , 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 using Newton's method of successive approximations, a The newton function can use either the recursive strategy of Project 2 or the iterative strategy of the Approximating Square Python's own estimate using math.sqrt. Roots Case Study. The task of testing for the limit is assigned to a function named limitReached , whereas the task of computing 11 a new approximation is assigned to a function named 12 import math improveEstimate. Each function expects the relevant |13 14 # Receive the input number from the user |15 x = float(input("Enter a positive number: ")) arguments and returns an appropriate value. 16 An example of the program input and output is shown below: 17 # Initialize the tolerance and estimate 18 tolerance = 0.000001

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Instructions newton.py 1 # Modify the code below 2 II I| || Restructure Newton's method (Case Study: Approximating 3 Program: newton.py Square Roots) by decomposing it into three cooperating 4 Author: Ken functions: newton , 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 8 Project 2 or the iterative strategy of the Approximating Square 9. Roots Case Study. The task of testing for the limit is assigned to a function named limitReached , whereas the task of computing 11 a new approximation is assigned to a function named 12 import math improveEstimate . Each function expects the relevant 13 arguments and returns an appropriate value. |14 # Receive the input number from the user 15 x = float(input("Enter a positive number: ")) 16 An example of the program input and output is shown below: 17 # Initialize the tolerance and estimate 18 tolerance = 0.000001 19 estimate = 1.0 Enter a positive number or enter/return to quit: 2 20 21 # Perform the successive approximations The program's estimate is 1.4142135623746899 22 while True: estimate = (estimate + x / estimate) / 2 difference if difference <= tolerance: 23 Python's estimate is 1.4142135623730951 Enter a positive number or enter/return to quit 24 abs (x - estimate ** 2) 25 26 break 27 28 # Output the result 29 print("The program's estimate is", estimate) 30 print("Python's estimate is ', math.sqrt(x))
Transcribed Image Text:Instructions newton.py 1 # Modify the code below 2 II I| || Restructure Newton's method (Case Study: Approximating 3 Program: newton.py Square Roots) by decomposing it into three cooperating 4 Author: Ken functions: newton , 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 8 Project 2 or the iterative strategy of the Approximating Square 9. Roots Case Study. The task of testing for the limit is assigned to a function named limitReached , whereas the task of computing 11 a new approximation is assigned to a function named 12 import math improveEstimate . Each function expects the relevant 13 arguments and returns an appropriate value. |14 # Receive the input number from the user 15 x = float(input("Enter a positive number: ")) 16 An example of the program input and output is shown below: 17 # Initialize the tolerance and estimate 18 tolerance = 0.000001 19 estimate = 1.0 Enter a positive number or enter/return to quit: 2 20 21 # Perform the successive approximations The program's estimate is 1.4142135623746899 22 while True: estimate = (estimate + x / estimate) / 2 difference if difference <= tolerance: 23 Python's estimate is 1.4142135623730951 Enter a positive number or enter/return to quit 24 abs (x - estimate ** 2) 25 26 break 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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