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9. (a) Using the standard Maclaurin series for ln(1 + x) write down the first four non-zero terms in the Maclaurin series for ln(2 + x). For what range of values of x does this series converge? Estimate the value of ln(2), given that ln(e) = 1, e≈ 2.7183.

9. (a) Using the standard Maclaurin series for ln(1 + x) write down the first four non-zero terms in the Maclaurin series for ln(2 + x). For what range of values of x does this series converge? Estimate the value of ln(2), given that ln(e) = 1, e≈ 2.7183.

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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9. (a) Using the standard Maclaurin series for ln(1 + x) write down the first four non-zero terms in the Maclaurin series for ln(2 + x). For what range of values of x does this series converge? Estimate the value of ln(2), given that ln(e) = 1, e≈ 2.7183.
Transcribed Image Text:9. (a) Using the standard Maclaurin series for ln(1 + x) write down the first four non-zero terms in the Maclaurin series for ln(2 + x). For what range of values of x does this series converge? Estimate the value of ln(2), given that ln(e) = 1, e≈ 2.7183.
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Can you explain why on step 2 you have added to first six terms? Why not four terms?

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