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Convert Newton's method for approximating square roots in Project 1 to a recursive function named newton . (Hint: The estimate of the square root should be passed as a second argument to the function.)

Convert Newton's method for approximating square roots in Project 1 to a recursive function named newton . (Hint: The estimate of the square root should be passed as a second argument to the function.)

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

Instructions newton.py + 1 # Modify the code below 2 II I| || Convert Newton's method for approximating square roots in Project 3 File: newton.py 1 to a recursive function named newton . (Hint: The estimate of the 4 Project 6.1 5 Compute the square root of a number (uses function with loop). 6 1. The input is a number, or enter/return to halt the input process. 8 2. The outputs are the program's estimate of the square root square root should be passed as a second argument to the function.) 7 An example of the program input and output is shown below: 9 using Newton's method of successive approximations, and Python's own estimate using math.sqrt. 10 11 "| Enter a positive number or enter/return to quit: 2 12 13 import math The program's estimate is 1.4142135623746899 14 Python's estimate is 1.4142135623730951 15 Enter a positive number or enter/return to quit 16 # Initialize the tolerance 17 TOLERANCE = 0.000001 18 19 def newton (x): 20 "I"Returns the square root of x.""" 21 # Perform the successive approximations estimate = 1.0 23 while True: (estimate + x / estimate) / 2 estimate ** 2) 24 estimate = difference = abs(x if difference <= TOLERANCE: 25 26 27 break 28 return estimate 29 30 def main(): 31 I" I|"Allows the user to obtain square roots.""" 32 while True: 33 # Receive the input number from the user 34 x = input("Enter a positive number or enter/return to quit: ") 35 if x == "": 36 break x = float(x) # Output the result print("The program's estimate is", newton(x)) print("Python's estimate is 37 38 39 40 ", math.sqrt(x)) 41 42 if --name_- %3D '-_main__": == 43 main()
Transcribed Image Text:Instructions newton.py + 1 # Modify the code below 2 II I| || Convert Newton's method for approximating square roots in Project 3 File: newton.py 1 to a recursive function named newton . (Hint: The estimate of the 4 Project 6.1 5 Compute the square root of a number (uses function with loop). 6 1. The input is a number, or enter/return to halt the input process. 8 2. The outputs are the program's estimate of the square root square root should be passed as a second argument to the function.) 7 An example of the program input and output is shown below: 9 using Newton's method of successive approximations, and Python's own estimate using math.sqrt. 10 11 "| Enter a positive number or enter/return to quit: 2 12 13 import math The program's estimate is 1.4142135623746899 14 Python's estimate is 1.4142135623730951 15 Enter a positive number or enter/return to quit 16 # Initialize the tolerance 17 TOLERANCE = 0.000001 18 19 def newton (x): 20 "I"Returns the square root of x.""" 21 # Perform the successive approximations estimate = 1.0 23 while True: (estimate + x / estimate) / 2 estimate ** 2) 24 estimate = difference = abs(x if difference <= TOLERANCE: 25 26 27 break 28 return estimate 29 30 def main(): 31 I" I|"Allows the user to obtain square roots.""" 32 while True: 33 # Receive the input number from the user 34 x = input("Enter a positive number or enter/return to quit: ") 35 if x == "": 36 break x = float(x) # Output the result print("The program's estimate is", newton(x)) print("Python's estimate is 37 38 39 40 ", math.sqrt(x)) 41 42 if --name_- %3D '-_main__": == 43 main()
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