f(x)=(3x+1) .a] Find the Taylor series expansion associated with f centered at 2.b] What is the largest interval on which the Taylor series expansion associated with f converges back to the function. Justify your answer as clearly as you can. **Hint:** Observe that \[ f(x) = \frac{1}{49} \left( 1 + \frac{3(x - 2)}{7} \right)^{-2} . \]This expression suggests a transformation applied to a function. The fraction and terms inside the brackets represent a shifted and scaled version of a parent function, and the negative exponent indicates an inverse squared relationship.

Answered: Image /qna-images/answer/c87b479d-6e7c-4515-84a5-664f2524bf96.jpgAs this extension is a polynomial of degree 1. It converges everywhere in Real line.

Answered: f(x)=(3x+1) . a] Find the Taylor series…

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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f(x)=(3x+1) .

a] Find the Taylor series expansion associated with f centered at 2.
b] What is the largest interval on which the Taylor series expansion associated with f converges back to the function. Justify your answer as clearly as you can.

**Hint:** Observe that

\[ f(x) = \frac{1}{49} \left( 1 + \frac{3(x - 2)}{7} \right)^{-2} . \]

This expression suggests a transformation applied to a function. The fraction and terms inside the brackets represent a shifted and scaled version of a parent function, and the negative exponent indicates an inverse squared relationship.

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