Letf(x) = ln(2x+1), x = (2,4).1. The Taylor polynomial T₂ (a) at the point aIn(7)+(2/7)*(x-3)-(2/49)*(x-3)^3 is2. The smallest value of M that occurs in Taylor's inequality is16/1253. With M having the above value, Taylor's inequality assures that theerror in the approximation f(x) ≈ T₂ (2) is less than8/375for all € (2,4).4. If (3,4) the Alternate Series Estimation Theorem assures thatthe error in the approximation f(x) T₂(2) is less than16/343Notice: Your input in 3. and 4. should contain the smallest possiblevalue, as indicated by Taylor Inequality and ASET.

Answered: Image /qna-images/answer/0fabc54a-8bfd-4283-ae82-2865d93f5a32.jpg

Let f(x) In(2x+1), (2,4). 1. The Taylor polynomial T₂ (2) at the point a In(7)+(2/7)*(x-3)-(2/49)*(x-3)^ 3 is 2. The smallest value of M that occurs in Taylor's inequality is 16/125

Let f(x) In(2x+1), (2,4). 1. The Taylor polynomial T₂ (2) at the point a In(7)+(2/7)(x-3)-(2/49)(x-3)^ 3 is 2. The smallest value of M that occurs in Taylor's inequality is 16/125

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 4E

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Question

Let
f(x) = ln(2x+1), x = (2,4).
1. The Taylor polynomial T₂ (a) at the point a
In(7)+(2/7)*(x-3)-(2/49)*(x-3)^
3 is
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 (2) is less than
8/375
for all € (2,4).
4. If (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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