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Home » Wait — earlier we missed \( m = 3 \ - Crosslake

Wait — earlier we missed \( m = 3 \ - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Solutions: \( u = 0 \), \( u = 2 \), \( u = 3 \)

📌 But \( v > 0 \), so \( u = \sqrt{v} > 0 \), thus \( u = 0 \) is invalid. Valid solutions: \( u = 2 \Rightarrow v = 4 \), \( u = 3 \Rightarrow v = 9 \)

📌 Sum of real roots: \( 4 + 9 = 13 \)

📌 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}

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