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*x-x' +x* -x' and |x|<0.2. 1+x Find the upper bound on the error if

*x-x' +x* -x' and |x|<0.2. 1+x Find the upper bound on the error if

Advanced Engineering Mathematics
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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Use the Macluarin series to solve:

**x-x +x -x' and x<0.2. 1+x Find the upper bound on the error if
Transcribed Image Text:**x-x +x -x' and x<0.2. 1+x Find the upper bound on the error if
Expert Solution
Step 1

Given : x1+x2≈x-x3+x5-x7 and x≤0.2

To find : upper bound on the error of the given Maclaurin series

Pre-requisite : 

1. Lagrange's formula : There is some number c between a and x such that 

                    Rnx=fn+1cn+1!x-an+1

2. Lagrange's formula to get a bound on the error Rnx : If a positive real number M exists such that fn+1c≤M for all c between a and x, then Lagrange's formula tells you that 

                   Rnx≤Mn+1!x-an+1

                                        

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