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f(x) = ln(2⋅ x + 1), x € (1, 3). 1. The Taylor polynomial T2 (x) at the point a = 2 is

f(x) = ln(2⋅ x + 1), x € (1, 3). 1. The Taylor polynomial T2 (x) at the point a = 2 is

Advanced Engineering Mathematics
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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Let f(x) = ln(2x+1), x = (1,3). 1. The Taylor polynomial T2 (x) at the point a = 2 is 2. The smallest value of M that occurs in Taylor's inequality is 3. With M having the above value, Taylor's inequality assures that the error in the approximation f(x) ≈ T2(x) is less than x = (1,3). for all 4. If x (2, 3) the Alternate Series Estimation Theorem assures that the error in the approximation f(x) ≈ T₂ (x) is less than Notice: Your input in 3. and 4. should contain the smallest possible value, as indicated by Taylor Inequality and ASET.
Transcribed Image Text:Let f(x) = ln(2x+1), x = (1,3). 1. The Taylor polynomial T2 (x) at the point a = 2 is 2. The smallest value of M that occurs in Taylor's inequality is 3. With M having the above value, Taylor's inequality assures that the error in the approximation f(x) ≈ T2(x) is less than x = (1,3). for all 4. If x (2, 3) the Alternate Series Estimation Theorem assures that the error in the approximation f(x) ≈ T₂ (x) is less than Notice: Your input in 3. and 4. should contain the smallest possible value, as indicated by Taylor Inequality and ASET.
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