Lecture 1: exercise solutions = sin(x) x² with an initial 1.ii. Use the Newton-Raphson method to determine the root of f(x) estimate of x = 1. The first step is to determine the derivative of f(x) with respect to x f'(x) = cos(x) - 2x. Using (9.4) we can then iteratively improve on our initial estimate for the solution to f(x). k Xk f(xk) Xk+1 1 1 -1.5853e-001 8.9140e-001 2 8.9140×10-1 -1.6637x10-² 8.7698x10-¹ 3 4 8.7698x10-1 -2.8815×10-4 8.7673x10-1 8.7673x10-1 -9.2541x10-8 8.7673x10-1 8.7673x10-1 -9.4369x10-15 8.7673x10-1 5

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