To create a power series for the 1 function f(x): = series for f(x)= (5-x)4 1 (5-x)³' O Differentiate the series for 1 f(x) = (5-x)³ result by -1. O Differentiate the series for 1 f(x) = (5-x)³ result by 3. Differentiate the series for 1 f(x) = (5-x)³ result by 3. O Differentiate the series for 1 f(x) = (5-x)³ result by -3. Differentiate the series for 1 f(x) = (5-x)³ result by -3. None of these. = from the we could then multiply the then multiply the then divide the , then multiply the then divide the 2
To create a power series for the 1 function f(x): = series for f(x)= (5-x)4 1 (5-x)³' O Differentiate the series for 1 f(x) = (5-x)³ result by -1. O Differentiate the series for 1 f(x) = (5-x)³ result by 3. Differentiate the series for 1 f(x) = (5-x)³ result by 3. O Differentiate the series for 1 f(x) = (5-x)³ result by -3. Differentiate the series for 1 f(x) = (5-x)³ result by -3. None of these. = from the we could then multiply the then multiply the then divide the , then multiply the then divide the 2
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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![### Creating a Power Series for a Given Function
To create a power series for the function:
\[ f(x) = \frac{1}{(5-x)^4} \]
from the series for:
\[ f(x) = \frac{1}{(5-x)^3}, \]
we could:
- **Option 1:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then multiply the result by -1.
- **Option 2:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then multiply the result by 3.
- **Option 3:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then divide the result by 3.
- **Option 4:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then multiply the result by -3.
- **Option 5:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then divide the result by -3.
- **Option 6:**
None of these.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55815b3c-2575-4201-a9dc-5a4b41a14c1d%2Fdfe0c608-ef3b-49de-a999-bb4087d4997f%2F5zdf4xk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Creating a Power Series for a Given Function
To create a power series for the function:
\[ f(x) = \frac{1}{(5-x)^4} \]
from the series for:
\[ f(x) = \frac{1}{(5-x)^3}, \]
we could:
- **Option 1:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then multiply the result by -1.
- **Option 2:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then multiply the result by 3.
- **Option 3:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then divide the result by 3.
- **Option 4:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then multiply the result by -3.
- **Option 5:**
Differentiate the series for
\[ f(x) = \frac{1}{(5-x)^3}, \]
then divide the result by -3.
- **Option 6:**
None of these.
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