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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
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
# 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.
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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