Steps: 1.What is the f" (x) of the function? 2. After getting the f"(x), what is the f"(a) of the function as a=1? + co ?(a) 3. After getting the f"(a), input it into the (numerator) of Taylor series expansion formula: E (x – a)", for n! (x - a)", a=1. 4. After getting the Taylorseries expansion, find the intervalof convergence (using Ratio Test). f(x)= log,(2x – 1) 2 f'(x)= In (6) (2x-1) 4 P"(x)= - In (6) (2x-1)2 16 p"(x}= In (6) (2x-1)3 96 p''(x)= - In (6) (2x-1)4 f"(x)=???? To get the f"(x), find the trend among the derivatives.

Steps: 1.What is the f" (x) of the function? 2. After getting the f"(x), what is the f"(a) of the function as a=1? + co ?(a) 3. After getting the f"(a), input it into the (numerator) of Taylor series expansion formula: E (x – a)", for n! (x - a)", a=1. 4. After getting the Taylorseries expansion, find the intervalof convergence (using Ratio Test). f(x)= log,(2x – 1) 2 f'(x)= In (6) (2x-1) 4 P"(x)= - In (6) (2x-1)2 16 p"(x}= In (6) (2x-1)3 96 p''(x)= - In (6) (2x-1)4 f"(x)=???? To get the f"(x), find the trend among the derivatives.

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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Question

100%

Steps:
1.What is the f" (x) of the function?
2. After getting the f"(x), what is the f"(a) of the function as a=1?
+ co
?(a)
3. After getting the f"(a), input it into the (numerator) of Taylor series expansion formula: E
(x – a)", for
n!
-
(x - a)", a=1.
4. After getting the Taylorseries expansion, find the intervalof convergence (using Ratio Test).
f(x)= log,(2x – 1)
2
f'(x)=
In (6) (2x-1)
4
P"(x)= -
In (6) (2x-1)2
16
p"(x}=
In (6) (2x-1)3
96
p''(x)= -
In (6) (2x-1)4
f"(x)=????
To get the f"(x), find the trend among the derivatives.

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