2. Suppose we wish to find the intersection of cos (ex) (where 0 < & << 1) and the straight line x by solving the equation X cos (ex) = 1. Using either the iterative method or a regular perturbation method, find the first three non-zero terms of the asymptotic series expansion of x. Hint: you may wish to use the expansion cosex ~ 1- 1 2 ε² + I 1 4! -4 ε+as ε → 0.
2. Suppose we wish to find the intersection of cos (ex) (where 0 < & << 1) and the straight line x by solving the equation X cos (ex) = 1. Using either the iterative method or a regular perturbation method, find the first three non-zero terms of the asymptotic series expansion of x. Hint: you may wish to use the expansion cosex ~ 1- 1 2 ε² + I 1 4! -4 ε+as ε → 0.
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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Transcribed Image Text:2. Suppose we wish to find the intersection of cos (ex) (where 0 < ɛ << 1) and the
straight line x by solving the equation
X
cos (ex)
= 1.
Using either the iterative method or a regular perturbation method, find the first three
non-zero terms of the asymptotic series expansion of x.
2
Hint: you may wish to use the expansion coSEX~ 1
²1/ε ² + 1 - £4
2
4!
I
ε+as ε → 0.
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