Maclaurin series

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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(a)
(b)
(c)
Use the Maclaurin series for e* to find the power series expansion of ex.
Using the first two non-zero terms of the expansion of ex, find an approximate
solution of the equation e¹/* = 1-ɛx, where a > 0 is a constant.
By sketching suitable graphs or otherwise, suggest when your approximate
solution may fail.
Transcribed Image Text:(a) (b) (c) Use the Maclaurin series for e* to find the power series expansion of ex. Using the first two non-zero terms of the expansion of ex, find an approximate solution of the equation e¹/* = 1-ɛx, where a > 0 is a constant. By sketching suitable graphs or otherwise, suggest when your approximate solution may fail.
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