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doubletree by hilton long island city new york - ECD Germany

📅 May 12, 2026 👤 scraface

May 12, 2026

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We aim to find $ \lim_{n \to \infty} b_n $.
First, observe that $ f(u) < u $ for all $ u > 0 $, since $ \frac{u^4}...
Taking limits on both sides of the recurrence:
\lim_{n \to \infty} b_{n+1} = \lim_{n \to \infty} f(b_n) = f(L).
But since $ \lim_{n \to \infty} b_{n+1} = \lim_{n \to \infty} b_n = L...
L = f(L) = L - \frac{L^4}{4} \Rightarrow \frac{L^4}{4} = 0 \Rightarrow...
Thus, the sequence converges to $ \boxed{0} $.
To confirm convergence, note that $ f(u) $ is continuous and decreasin...
Question: Let $ p(x) $ be a polynomial such that
p(x) = x^3 - 3x^2 + 5x - 7,

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