Newton-Raphson Method
Version 1.13Interactive tangent-method simulator for approximating solutions of \(f(x)=0\).
\[x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}\]
Examples: x^2-2, x^3-x-2, cos(x)-x. You can write 2x or 2*x; use a decimal point.
Function and Tangent Graph
Final Summary
Last approximation—
Residual |f(x)|—
Iterations performed—
Iteration Table
| n | xₙ | f(xₙ) | f′(xₙ) | xₙ₊₁ | |Δx| |
|---|
How It Works
I choose an initial approximation x₀ and draw the tangent to the curve at (x₀, f(x₀)). Where the tangent intersects the x-axis gives the next approximation. I repeat until the required tolerance is met or the iteration limit is reached.
The method may fail to converge; a zero or very small derivative can prevent further calculations. The graph scale stays fixed throughout the simulation.