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
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
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 \( \lim_{t \to \infty} x_t \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc931b694-aaff-47c2-895e-73bc1d52993a%2Fe115f459-6771-4f63-a848-3b68eb738789%2Fdb1z3c5_processed.png&w=3840&q=75)
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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