Consider the function f(x) = xlog(x). Let T(x) denote the Taylor of order n for f(x) about x = 1. approximation Find the following: T₁ (2)= T₂ (2) = T3 (2) = Use 3 decimal places in your answer, but make sure you carry all decimals when performing calculations The approximation T3 (2) is . ? • greater than • • equal to the exact value f(2). less than In the definition f(x) = Tn(x) + En(x), the Lagrange Remain- der Formula provides the estimate E3 (2)| ≤
Consider the function f(x) = xlog(x). Let T(x) denote the Taylor of order n for f(x) about x = 1. approximation Find the following: T₁ (2)= T₂ (2) = T3 (2) = Use 3 decimal places in your answer, but make sure you carry all decimals when performing calculations The approximation T3 (2) is . ? • greater than • • equal to the exact value f(2). less than In the definition f(x) = Tn(x) + En(x), the Lagrange Remain- der Formula provides the estimate E3 (2)| ≤
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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Transcribed Image Text:Consider the function f(x) = xlog(x). Let T₂(x) denote the
Taylor
of order n for f(x) about x = 1.
approximation
Find the following:
T₁ (2)=
T₂ (2) =
T3 (2) =
Use 3 decimal places in your answer, but make sure you carry
all decimals when performing calculations
The approximation T3 (2) is
• ?
• greater than
• less than
• equal to
the exact value f(2).
In the definition f(x) = T₂(x) + En(x), the Lagrange Remain-
der Formula provides the estimate
E3 (2)| ≤.
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