Let f(x) = ln(2x+1), x = (2,4). 1. The Taylor polynomial T₂ (2) at the point a = 3 is In(7)+(2/7)*(x-3)-(2/49)*(x-3)^ 2. The smallest value of M that occurs in Taylor's inequality is 16/125 3. With M having the above value, Taylor's inequality assures that the error in the approximation f(x) ≈ T2(x) is less than 8/375 for all x € (2,4). 4. If Є (3, 4) the Alternate Series Estimation Theorem assures that the error in the approximation f(x) T₂(2) is less than 16/343 Notice: Your input in 3. and 4. should contain the smallest possible value, as indicated by Taylor Inequality and ASET.
Let f(x) = ln(2x+1), x = (2,4). 1. The Taylor polynomial T₂ (2) at the point a = 3 is In(7)+(2/7)*(x-3)-(2/49)*(x-3)^ 2. The smallest value of M that occurs in Taylor's inequality is 16/125 3. With M having the above value, Taylor's inequality assures that the error in the approximation f(x) ≈ T2(x) is less than 8/375 for all x € (2,4). 4. If Є (3, 4) the Alternate Series Estimation Theorem assures that the error in the approximation f(x) T₂(2) is less than 16/343 Notice: Your input in 3. and 4. should contain the smallest possible value, as indicated by Taylor Inequality and ASET.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Let
f(x) = ln(2x+1), x = (2,4).
1. The Taylor polynomial T₂ (2) at the point a = 3 is
In(7)+(2/7)*(x-3)-(2/49)*(x-3)^
2. The smallest value of M that occurs in Taylor's inequality is
16/125
3. With M having the above value, Taylor's inequality assures that the
error in the approximation f(x) ≈ T2(x) is less than
8/375
for all x € (2,4).
4. If Є (3, 4) the Alternate Series Estimation Theorem assures that
the error in the approximation f(x) T₂(2) is less than
16/343
Notice: Your input in 3. and 4. should contain the smallest possible
value, as indicated by Taylor Inequality and ASET.
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