Newton's Method
Find roots using Newton-Raphson method
Examples: sin(x), exp(-x^2), ln(x), sqrt(x), pi
Converged
Numerical estimate: 1.41421356237
Residual f(x)
4.51061410445e-12
Iterations
4
Reason
Convergence conditions were not met
Method: Newton iteration with an adaptive numerical derivative
This is a finite-sample numerical approximation, not symbolic calculus or a proof that a limit exists. Check discontinuities and the reported error estimate.