Find the equilibria of the difference equation xt+1 = stable or unstable. If xo = 1/2 what is lim x? t→∞ 4xt 1 + 5xt and classify them as

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**Problem:** Find the equilibria of the difference equation \( x_{t+1} = \frac{4x_t}{1 + 5x_t} \) and classify them as stable or unstable. If \( x_0 = \frac{1}{2} \), what is \( \lim_{t \to \infty} x_t \)?
Transcribed Image Text:**Problem:** Find the equilibria of the difference equation \( x_{t+1} = \frac{4x_t}{1 + 5x_t} \) and classify them as stable or unstable. If \( x_0 = \frac{1}{2} \), what is \( \lim_{t \to \infty} x_t \)?
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