5. Binomial Expansion In the previous problem it was suggested to use
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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
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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