# Untitled

unknown
c_cpp
2 years ago
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```#include <bits/stdc++.h>
using namespace std;

float f(float x) // f(x) function.
{
return sin(x) * sin(x) + x - 1; // insert your equation here.
}
float df(float x) // f'(x) function.
{
return sin(2 * x) + 1; // insert the first derivative of your equation here.
}
void newton_raphson(float x0) // Main Algorithm of newton_raphson method.
{
printf("---------------------------\nRoot using Newton-Raphson Method\n---------------------------\n");
int iteration = 1; // for counting iteration.

float x1; // x_n+1 declaration.

while (1) // infinite loop. This will run until we found the desirable result.
{
x1 = x0 - (f(x0) / df(x0)); // Main formula of newton raphson method.  ( x_n+1 = x_n - (f(x_n)/ f'(x_n)));

printf(" Iteration = %d\tx0 = %.5f\tx1 = %.5f\tf(x1) = %.5f\n", iteration, x0, x1, f(x1)); // printing results.

if (abs(f(x1)) == 0)
{
break; // if we found the root loop will be terminated.
}
else
{
x0 = x1;
}
iteration++;
}
cout << "The smallest root: " << x1 << '\n';
}

int main()
{
float x0, x1;
cout << "Enter your initial guess: ";
cin >> x0;
newton_raphson(x0);
}```