Consider T3 (x), the 3rd degree Taylor polynomial of f(x) = In(1+ 2x) centered at a = 1 . Use the Taylor Polynomial Error Bound to estimate the accuracy of the approximation f(x) - T3(x) for 1

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider T3 (x), the 3rd degree Taylor polynomial of f(x) = In(1+ 2x) centered at a = 1.
Use the Taylor Polynomial Error Bound to estimate the accuracy of the approximation f() ~ T3(x) for
1<x < 2. As always, be sure to give an exact answer, a decimal approximation is not enough and not needed.
(Your answer should not depend on x or n.)
|error| <
625
4
lerror| <
125
64
|error| <
81
4
lerror| <
81
lerror| <
1/6
Transcribed Image Text:Consider T3 (x), the 3rd degree Taylor polynomial of f(x) = In(1+ 2x) centered at a = 1. Use the Taylor Polynomial Error Bound to estimate the accuracy of the approximation f() ~ T3(x) for 1<x < 2. As always, be sure to give an exact answer, a decimal approximation is not enough and not needed. (Your answer should not depend on x or n.) |error| < 625 4 lerror| < 125 64 |error| < 81 4 lerror| < 81 lerror| < 1/6
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