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5. Binomial Expansion In the previous problem it was suggested to use

5. Binomial Expansion In the previous problem it was suggested to use

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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5. Binomial Expansion In the previous problem it was suggested to use (1 – x)" - 1 – nx which olds for any number n and any x much smaller than 1 (that is lxl << 1). Make a table showing (1 - x)" and its approximation (1 - nx) for the case n = -1/2 and x = 0.5,0.1,0.01, and 0.001. In each case find the percentage by which the approximation differs from the exact result. Hint: In this case neglect significant figures and use enough digits so that you can actually see a difference.
Transcribed Image Text:5. Binomial Expansion In the previous problem it was suggested to use (1 – x)" - 1 – nx which olds for any number n and any x much smaller than 1 (that is lxl << 1). Make a table showing (1 - x)" and its approximation (1 - nx) for the case n = -1/2 and x = 0.5,0.1,0.01, and 0.001. In each case find the percentage by which the approximation differs from the exact result. Hint: In this case neglect significant figures and use enough digits so that you can actually see a difference.
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