Consider the following function. f(x) = x In(2x), a = 1, n = 3, 0.5 s xs 1.5 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) = T,(x) when x lies in the given interval. (Round your answer to four decimal places.) |R3(x)| S|

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 the following function.
f(x) = x In(2x),
a = 1,
n = 3,
0.5 < x < 1.5
(a) Approximate f by a Taylor polynomial with degree n at the number a.
T3(x) =
(b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) × T„(x) when x lies in the given interval. (Round your answer to four decimal places.)
|R3(x)| <
Transcribed Image Text:Consider the following function. f(x) = x In(2x), a = 1, n = 3, 0.5 < x < 1.5 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) × T„(x) when x lies in the given interval. (Round your answer to four decimal places.) |R3(x)| <
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