Question: The functions f (x) = x 2 - 4 and g (x) = (x - 2) 2 both have a zero at x = 2.

The functions f (x) = x² - 4 and g (x) = (x - 2)² both have a zero at x = 2. Apply the Newton–Raphson algorithm to each function with x₀ = 3, and determine the value of n for which xn appears on the screen as exactly 2. Graph the two functions and explain why the sequence for f(x) converges so quickly to 2, whereas the sequence for g(x) converges so slowly.

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