For each integer k = 1,2, 3, ... and each choice of + or –, determine the stability of x = 0 as a fixed point of the equation i = ±a* Restricting to the cases where x = 0 is stable, does making k larger result in faster or slower convergence to the fixed point? Give both a heuristic explanation and one in terms of the exact solutions. (Note that this equation is separable.)

For each integer k = 1,2, 3, ... and each choice of + or –, determine the stability of x = 0 as a fixed point of the equation i = ±a* Restricting to the cases where x = 0 is stable, does making k larger result in faster or slower convergence to the fixed point? Give both a heuristic explanation and one in terms of the exact solutions. (Note that this equation is separable.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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