1. Let the number be a (you are given that a 0 2·Let zo = 1. d Cunpate saccesiwe

Question

1. Let the number be a (you are given that a 0 2·Let zo = 1. d Cunpate saccesiwet 01 T- 4. The iteration clearly goes on forever, so we set a tolerance to stop the iteration 5. Stop the iteration whe ri-1l s 104, 6. Return the value of r, as the approximation to the square root a Write a function to implement the Babylonian algorithm to calculate the square root of a positive nmber double sqrt Babylonian (double a); The function return value is the approximation r, to the square root of a Print the values of the iterates r, inside your function, starting with ro Submit your function code as your answer.

Explanation / Answer

Find the required program in C++:

//===========================================================

#include <iostream>
#include <math.h> // Required to calculate absolute value of double type variables

using namespace std;

double sqrt_Babylonian(double a)
{
    double x_prev,x_current;
    int i=0;
    x_prev=1;   // x0 = 1
    while(1)
    {
        std::cout << "Value of x("<<i<<") is: "<< x_prev << std::endl;
        x_current = (0.5)*(x_prev + (a/x_prev)); // Iterative approximation
        if(fabs(x_prev-x_current)<=0.0001) // Tolerance check
        {
            break;
        }
        x_prev=x_current;
        i=i+1;
    }
    return(x_current);
}
int main() {
    double a;
    std::cout << "Please enter the value of 'a': " << std::endl;
    std::cin >> a;
    std::cout << "The approximate value of a^(1/2) as returned by function is:"<<sqrt_Babylonian(a) << std::endl;
return 0;
}

//==========================================================

Sample output for a=2;

Please enter the value of 'a': 2
Value of x(0) is: 1
Value of x(1) is: 1.5
Value of x(2) is: 1.41667
Value of x(3) is: 1.41422
The approximate value of a^(1/2) as returned by function is:1.41421

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