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fly new york to buffalo - NBX Soluciones

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: A plant biologist studying drought resistance defines a function \( f(t) = t - rac{t^3}{6} \) to model stress response. Define \( c_n \) by \( c_1 = 0.5 \) and \( c_{n+1} = f(c_n) \). Determine \( \lim_{n o \infty} c_n \), assuming convergence.

📌 Solution: Assume \( \lim_{n o \infty} c_n = L \). Then taking limits:

📌 L = f(L) = L - rac{L^3}{6}

📌 \Rightarrow 0 = -rac{L^3}{6}

📌 \Rightarrow L^3 = 0 \Rightarrow L = 0

📌 We verify convergence. Since \( f(t) = t\left(1 - rac{t^2}{6}

📌 ight) \), for \( t > 0 \), \( f(t) < t \) when \( 1 - rac{t^2}{6} < 1 \), which is always true, but more importantly, for \( t \in (0, \sqrt{6}) \), \( c_{n+1} = f(c_n) < c_n \). With \( c_1 = 0.5 \), compute:

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