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
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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Question
100%
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0af76125-3c89-4399-ba95-fec40f6dede7%2Fe92e87f2-e9a3-4f63-9b70-4f834f145c6a%2Furyxjaf_processed.png&w=3840&q=75)
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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Follow-up Question
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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