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Show me the steps of determine yellow

Show me the steps of determine yellow

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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Show me the steps of determine yellow

Hence we obtain the linearized equation of Eq.(8) about its unique positive equilibrium point j as follow: 2p Zn + 72 n-m Zn+1 0. (15) Yn Yn+1 = 1+p2 Yn-m (8) 4 Stability of Eq.(8) In this here, we study the stability of Eq.(8). Firstly we handle the linearized equation of Eq.(8) about its unique positive equilibrium point. Let I be some interval of real numbers and let f: Im+1 - I be a continuously differentiable function such that f is defined by Yn (Yn, Yn-1,* , Yn-m) = 1+p Yn-m Therefore we have af go = dyn 91 = 92 = . = qm-1 = 0, af Əyn-m 2p 9m = Hence we obtain the linearized equation of Eq.(8) about its unique positive equilibrium point j as follow: 2p n-m = 0. (15) Zn+1 - Zn + Therefore, the characteristic equation of Eq.(8) is Am+1 - 2p = 0. (16)
Transcribed Image Text:Hence we obtain the linearized equation of Eq.(8) about its unique positive equilibrium point j as follow: 2p Zn + 72 n-m Zn+1 0. (15) Yn Yn+1 = 1+p2 Yn-m (8) 4 Stability of Eq.(8) In this here, we study the stability of Eq.(8). Firstly we handle the linearized equation of Eq.(8) about its unique positive equilibrium point. Let I be some interval of real numbers and let f: Im+1 - I be a continuously differentiable function such that f is defined by Yn (Yn, Yn-1,* , Yn-m) = 1+p Yn-m Therefore we have af go = dyn 91 = 92 = . = qm-1 = 0, af Əyn-m 2p 9m = Hence we obtain the linearized equation of Eq.(8) about its unique positive equilibrium point j as follow: 2p n-m = 0. (15) Zn+1 - Zn + Therefore, the characteristic equation of Eq.(8) is Am+1 - 2p = 0. (16)
Theorem 10 Every solution of Eq.(8) satisfies both of the following asymptotic relations Yn+1 – lim Уп — у n-00 lim sup (lyn – ỹ|)'/" where je {1, ·. . , k} and X; are the roots of characteristic equation (16).
Transcribed Image Text:Theorem 10 Every solution of Eq.(8) satisfies both of the following asymptotic relations Yn+1 – lim Уп — у n-00 lim sup (lyn – ỹ|)'/" where je {1, ·. . , k} and X; are the roots of characteristic equation (16).
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