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1. Use the Maclaurin Series to approximate the function f (x) = In(1+ x) using each of the combinations of approximation order and step size. For each approximation, calculate the relative truncation error to three significant figures. Approximation Step size, Relative Order h Maclaurin Series Truncation Error O(h) O(h) O (h) O(h) O(h?) O(h?) O(h²) O(h²) 0.25 0.5 1.0 1.5 0.25 0.5 1.0 1.5

1. Use the Maclaurin Series to approximate the function f (x) = In(1+ x) using each of the combinations of approximation order and step size. For each approximation, calculate the relative truncation error to three significant figures. Approximation Step size, Relative Order h Maclaurin Series Truncation Error O(h) O(h) O (h) O(h) O(h?) O(h?) O(h²) O(h²) 0.25 0.5 1.0 1.5 0.25 0.5 1.0 1.5

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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Truncation Error 1

Use the Maclaurin Series to approximate the function f (x) = In(1+ x) using each of the combinations of approximation order and step size. For each approximation, calculate the relative truncation error to three significant figures. 1. Approximation Step size, Relative Order h Maclaurin Series Truncation Error O (h) O(h) O (h) O(h) O(h?) O(h?) O(h²) O (h²) 0.25 0.5 1.0 1.5 0.25 0.5 1.0 1.5 What can you conclude about the relationship between the approximation order, step size, and truncation error? Are higher-order approximation orders always better?
Transcribed Image Text:Use the Maclaurin Series to approximate the function f (x) = In(1+ x) using each of the combinations of approximation order and step size. For each approximation, calculate the relative truncation error to three significant figures. 1. Approximation Step size, Relative Order h Maclaurin Series Truncation Error O (h) O(h) O (h) O(h) O(h?) O(h?) O(h²) O (h²) 0.25 0.5 1.0 1.5 0.25 0.5 1.0 1.5 What can you conclude about the relationship between the approximation order, step size, and truncation error? Are higher-order approximation orders always better?
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