Evaluate e^-6 with the two forms of series expansion shown, compare them to the true value of 2.478752177 x10^-3.use 5 terms to evaluate each series and compute the approximate and true relative errors Evaluate e^-6 with the two forms of series expansion shown, compare them to the true valueof 2.478752177 x10^-3.use 5 terms to evaluate each series and compute the approximate and true relative errorse¹=1-x€²= 1/- =+3!

Answered: Evaluate e^-6 with the two forms of…

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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Question

Evaluate e^-6 with the two forms of series expansion shown, compare them to the true value of 2.478752177 x10^-3.
use 5 terms to evaluate each series and compute the approximate and true relative errors

Expert Solution

Step 1

What is Error:

Error is the difference between a genuine value and an estimate, or approximate, representation of that value in practical mathematics. The discrepancy between the mean of the complete population and the mean of a sample taken from that population is a frequent example in statistics. When an infinite series is ignored for all but a small number of terms, a truncation error occurs.

To Determine:

We determine the value of $e^{- 6}$ using two different infinite series taking first term. Then, we determine the approximate and true relative error by comparing the approximate values with true value of $e^{- 6}$ given as $0.002478752177$ .