der the Taylor expansions of the functions y, = e and y, = cos x about x = 0. Find an approximate series expansion p(x) for y = e* cos x with an order of approximation 0(h*) using the above Taylor expansions. What is the relative error resulting in approximating y(1.1) by the expansion in part a) ?

der the Taylor expansions of the functions y, = e and y, = cos x about x = 0. Find an approximate series expansion p(x) for y = e* cos x with an order of approximation 0(h*) using the above Taylor expansions. What is the relative error resulting in approximating y(1.1) by the expansion in part a) ?

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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Question

Consider the Taylor expansions of the functions y, = e* and y2 = cos x about x = 0.
a) Find an approximate series expansion p(x) for y = e* cos x with an order of approximation 0(h*) using the
above Taylor expansions.
b) What is the relative error resulting in approximating y(1.1) by the expansion in part a) ?
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