Answer:
import math
tolerance=0.00001
approximation=1.0
x = float(input("Enter a positive number: "))
def newton(number,approximation):
approximation=(approximation+number/approximation)/2
difference_value =abs(number-approximation**2)
if difference_value<= tolerance:
return approximation
else:
return newton(number,approximation)
print("The approximation of program = ", newton(x, approximation))
print("The approximation of Python = ", math.sqrt(x))
Explanation:
- Create a recursive function called newton that calls itself again and again to approximate square root for the newton technique.
- Apply the formulas to find the estimate value and the difference value
.
- Check whether the difference_value is less than the tolerance value and then return the value of approximation else make a recursive call to the newton function by passing the user input and the new approximation value
.
- Finally display all the results using the print statement.
