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For the given function y(x) = - cos x² - In (1-x²) x" a) Find the Maclaurin series up to x inclusive using the Macla functions.

For the given function y(x) = - cos x² - In (1-x²) x" a) Find the Maclaurin series up to x inclusive using the Macla functions.

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 7: For the given function y(x): - cos x² - In (1-x²) a) Find the Maclaurin series up to x inclusive using the Maclaurin series of elementary functions. b) Find the limit of y(x) when x → 0 in the exact form (don't use a calculator). c) Using the Maclaurin series and keeping only the first three nonzero terms, calculate the 1/2 approximate value of the integral I = y(x) dx up to four significant figures. Tyx 0
Transcribed Image Text:Question 7: For the given function y(x): - cos x² - In (1-x²) a) Find the Maclaurin series up to x inclusive using the Maclaurin series of elementary functions. b) Find the limit of y(x) when x → 0 in the exact form (don't use a calculator). c) Using the Maclaurin series and keeping only the first three nonzero terms, calculate the 1/2 approximate value of the integral I = y(x) dx up to four significant figures. Tyx 0
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