Question

Restructure Newton's method (Case Study: Approximating Square Roots) by decomposing it into three cooperating functions.

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 to quit
Restructure Newton's method (Case Study: Approximating Square Roots) by decomposing it into three cooperating functions. The nevton 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 improveEstinate. 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 progran's estinate is 1.4142135623746899 Python's estinate is 1.4142135623730951 Enter a positive number or enter/return to quit

Answer 1

thanks for the question, here is the code in python

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import math
def limitReached(val,last):

    return abs(val - last) < 1e-2

def improvateEstimate(val,n):
    return (val + n / val) * 0.5


def squareroot(n):
    val = n
    while True:
        last = val
        val = improvateEstimate(val,n)
        if limitReached(val,last):
            break
    return val

while True:
    n=(input(' Enter a positive number or enter/return to quit: '))
    if n=='':
        break
    else:
        print('The program\'s estimate is :',squareroot(eval(n)))
        print('Python\'s estimate is      :', math.sqrt(eval(n)))
        print()

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