Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.7 Newton’s Method (and Chaos), #23 · Calculus · Applications of derivatives

For … when does … blow up

This problem is about $x^{2} + 1 = 0$ and chaos.

For $θ = π /16$ when does $x_{n} = cot 2^{n} θ$ blow up? For $θ = π /7$ when does $cot 2^{n} θ = cot θ$ ? (The angles $2^{n} θ$ and $θ$ differ by a multiple of $π$ .)

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.7 Newton’s Method (and Chaos), #23

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