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Consider the functions y D. For y = A. Write the Taylor expansions for the two functions about = 0. What is similar about the two series? What is different? 1 1 + x² B. Looking at the series, which function do you predict will be greater over the interval (−1, 1)?| and y = 1 - sin(x²). 1 , the radius of convergence is R = 1+z² C. Are these functions even or odd? E. For y = 1 - sin(2²), the radius of convergence is R = [ (type inf if the radius of convergence is infinite to get ∞o). (type inf if the radius of convergence is infinite to get ∞o).

Consider the functions y D. For y = A. Write the Taylor expansions for the two functions about = 0. What is similar about the two series? What is different? 1 1 + x² B. Looking at the series, which function do you predict will be greater over the interval (−1, 1)?| and y = 1 - sin(x²). 1 , the radius of convergence is R = 1+z² C. Are these functions even or odd? E. For y = 1 - sin(2²), the radius of convergence is R = [ (type inf if the radius of convergence is infinite to get ∞o). (type inf if the radius of convergence is infinite to get ∞o).

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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Consider the functions y D. For y = A. Write the Taylor expansions for the two functions about = 0. What is similar about the two series? What is different? 1 1 + x² B. Looking at the series, which function do you predict will be greater over the interval (-1, 1)? and y = 1 - sin(x²). 1 , the radius of convergence is R = 1+x²¹ C. Are these functions even or odd? E. For y = 1 - sin(2²), the radius of convergence is R = | (type inf if the radius of convergence is infinite to get ∞o). (type inf if the radius of convergence is infinite to get ∞o). Looking at the relative sizes of the successive terms in your series, note how the radii of convergence you found make sense.
Transcribed Image Text:Consider the functions y D. For y = A. Write the Taylor expansions for the two functions about = 0. What is similar about the two series? What is different? 1 1 + x² B. Looking at the series, which function do you predict will be greater over the interval (-1, 1)? and y = 1 - sin(x²). 1 , the radius of convergence is R = 1+x²¹ C. Are these functions even or odd? E. For y = 1 - sin(2²), the radius of convergence is R = | (type inf if the radius of convergence is infinite to get ∞o). (type inf if the radius of convergence is infinite to get ∞o). Looking at the relative sizes of the successive terms in your series, note how the radii of convergence you found make sense.
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