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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

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

C++ Programming: From Problem Analysis to Program Design
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter15: Recursion
Section: Chapter Questions
Problem 15SA
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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.) 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
Transcribed Image Text: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.) 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
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What should be the correct code below with the same problem? 
 
import math


# Initialize the tolerance
TOLERANCE = 0.000001

def newton(x):
    """Returns the square root of x."""
    # Perform the successive approximations
    estimate = 1.0
    while True:
        estimate = (estimate + x / estimate) / 2
        difference = abs(x - estimate ** 2)
        if difference <= TOLERANCE:
            break
    return estimate

def main():
    """Allows the user to obtain square roots."""
    while True:
        # Receive the input number from the user
        x = input("Enter a positive number or enter/return to quit: ")
        if x == "":
             break
        x = float(x)
        # Output the result
        print("The program's estimate is", newton(x))
        print("Python's estimate is     ", math.sqrt(x))

if __name__ == "__main__":
    main()
 
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