The Newton-Raphson method for finding the root of $f(x) = 0$ has what order of convergence near a simple real root?

(A) 2 (Quadratic)

(B) 1 (Linear)

(C) 3 (Cubic)

(D) 1.618 (Superlinear)

Answer Key:

A

### Solution: For a simple root ($f'(x^*) \neq 0$), the Newton-Raphson method converges quadratically (order 2). Correct: A.

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