Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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# 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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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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