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3. Consider the Maclaurin expansion cos(x²) = numbers x. (a) Use this expansion to give the first three terms of a power series expansion for ƒ cos(x²) dx. = 1- 21+30- +... valid for all real 3 2! 6! (b) Use your expansion in part (a) to approximate ¹⁹ cos(x²) dx. Again, use three terms. Round your answer to four decimal places. (c) Use the Alternating Series Estimation Theorem to give an upper bound on the error in your estimate in part (b).

3. Consider the Maclaurin expansion cos(x²) = numbers x. (a) Use this expansion to give the first three terms of a power series expansion for ƒ cos(x²) dx. = 1- 21+30- +... valid for all real 3 2! 6! (b) Use your expansion in part (a) to approximate ¹⁹ cos(x²) dx. Again, use three terms. Round your answer to four decimal places. (c) Use the Alternating Series Estimation Theorem to give an upper bound on the error in your estimate in part (b).

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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ร x8 x12 + 2! 4! 6! 3. Consider the Maclaurin expansion cos(x²) = 1 numbers x. (a) Use this expansion to give the first three terms of a power series expansion for f cos(x²) dx. + valid for all real 2 0.9 (b) Use your expansion in part (a) to approximate ſºº cos(x²) dx. Again, use three terms. Round your answer to four decimal places. (c) Use the Alternating Series Estimation Theorem to give an upper bound on the error in your estimate in part (b).
Transcribed Image Text:ร x8 x12 + 2! 4! 6! 3. Consider the Maclaurin expansion cos(x²) = 1 numbers x. (a) Use this expansion to give the first three terms of a power series expansion for f cos(x²) dx. + valid for all real 2 0.9 (b) Use your expansion in part (a) to approximate ſºº cos(x²) dx. Again, use three terms. Round your answer to four decimal places. (c) Use the Alternating Series Estimation Theorem to give an upper bound on the error in your estimate in part (b).
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