Find a geometric power series for the functions, centered at c = 0 unless a different c is specified. a. f(x)= 1 2-x 3 2x-1 f. f(x)=;
Find a geometric power series for the functions, centered at c = 0 unless a different c is specified. a. f(x)= 1 2-x 3 2x-1 f. f(x)=;
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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Transcribed Image Text:# Geometric Power Series for Functions
This module provides exercises on finding a geometric power series for a given set of functions. Each function is centered at \( c = 0 \) unless otherwise specified.
## Exercise 4
Find a geometric power series for the following functions, centered at \( c = 0 \) unless a different \( c \) is specified:
a. \( f(x) = \frac{1}{2 - x} \)
b. \( f(x) = \frac{3}{2x - 1}, \, c = 2 \)
f. \( f(x) = \frac{3}{2x - 1} \)
g. \( f(x) = \frac{3x}{x^2 + x - 2} \)
### Instructions:
- Determine the geometric power series representation for each function.
- For example, start by rewriting the functions in the standard geometric series form if possible.
- Pay close attention to any specified center \( c \), as it may modify the form of the series.
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