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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/6/a/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 2 / 6 / a / Solution by

Codex  0 2026-10-18

Setting the tangent line approximation equal to zero gives the Newton root-finding iteration

x_{1} = x_{0} - \frac{f ( x _{0} )}{f ^{'} ( x _{0} )} .

The step requires a nonzero derivative at the starting point.

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