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Estimating errors Use the remainder term to estimate the
Chapter 7, Problem 49E(choose chapter or problem)
Estimating errors Use the remainder term to estimate the absolute error in approximating the following quantities with the nth-order Taylor polynomial centered at 0. Estimates are not unique.
\(e^{0.25} ; n=4\)
Questions & Answers
QUESTION:
Estimating errors Use the remainder term to estimate the absolute error in approximating the following quantities with the nth-order Taylor polynomial centered at 0. Estimates are not unique.
\(e^{0.25} ; n=4\)
ANSWER:Solution 49E
Step 1:
In this problem we have to find the absolute error using remainder term in approximating with the
-order Taylor polynomial centered at 0.
Let us first find the order Taylor polynomial of
centered at 0.
Taylor series is given by .
In our case
So, what we need to do to get desired polynomial is to calculate derivatives, evaluate them at the given point and plug results into given formula.