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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).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 76E
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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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