Newton-Raphson Calculator
Find roots of functions using the Newton-Raphson iterative method.
Function f(x) = 0
Newton-Raphson Formula
x_{n+1} = x_n - f(x_n) / f'(x_n)
Supported Functions
Operators: + - * / ^
Functions: sin, cos, tan, log, exp, sqrt, abs
Constants: pi, e
Example: x^3 - 2*x + sin(x)
Convergence
Quadratic convergence near simple roots
Error at step n+1 ≈ C × (error at step n)²
Requires good initial guess
Root Found
x = 1.5213797068
f(x) = 4.0856e-14
Iterations
3
Final Error
9.9158e-8
Iteration History
| n | xₙ | f(xₙ) | Error |
|---|---|---|---|
| 0 | 1.50000000 | -1.2500e-1 | 2.1739e-2 |
| 1 | 1.52173913 | 2.1369e-3 | 3.5932e-4 |
| 2 | 1.52137981 | 5.8937e-7 | 9.9158e-8 |
Convergence Analysis
e_1/e_0²:0.7603
e_2/e_1²:0.7680
Constant ratio confirms quadratic convergence