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Recall the power series expansion for cos x = 1 2! 4! 6! i.) Use the given expansion to derive a power series expansion for cos(2x). 1 A. 1 – x² + 12 1 9* xº + 360 4 B. 1 – 2x +* - + | 45 2 4 C. 1 + 2x² + + .. 45 1 D. 1 + x² + 12 + 360 2x4 2x2 Е. 1 — 2! 2x6 + ... 4! 6! Enter your answer choice as "A", "B", "C", "D" or "E": ii.) Use the first 3 terms in the expansion in part (a.) to approximate • 0.9 cos(2x) dx. Give your answer as a decimal value rounded to 6 decimal places.

Recall the power series expansion for cos x = 1 2! 4! 6! i.) Use the given expansion to derive a power series expansion for cos(2x). 1 A. 1 – x² + 12 1 9* xº + 360 4 B. 1 – 2x +* - + | 45 2 4 C. 1 + 2x² + + .. 45 1 D. 1 + x² + 12 + 360 2x4 2x2 Е. 1 — 2! 2x6 + ... 4! 6! Enter your answer choice as "A", "B", "C", "D" or "E": ii.) Use the first 3 terms in the expansion in part (a.) to approximate • 0.9 cos(2x) dx. Give your answer as a decimal value rounded to 6 decimal places.

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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Recall the power series expansion for cos x = 2! 6! i.) Use the given expansion to derive a power series expansion for cos(2x). 1 A. 1 – x? + 12 1 x° + .. 360 2 4 B. 1 – 2x +x* 4 gt. - 45 2 C. 1 + 2x² + 4 X° + • 45 D. 1 + x² + 12 1 + 360 .4 + .. 2x2 Е. 1 - 2! 2x4 2x6 4! 6! Enter your answer choice as "A", "B", "C", "D" or "E": ii.) Use the first 3 terms in the expansion in part (a.) to approximate 0.9 cos(2x) dx. Give your answer as a decimal value rounded to 6 decimal places. +
Transcribed Image Text:Recall the power series expansion for cos x = 2! 6! i.) Use the given expansion to derive a power series expansion for cos(2x). 1 A. 1 – x? + 12 1 x° + .. 360 2 4 B. 1 – 2x +x* 4 gt. - 45 2 C. 1 + 2x² + 4 X° + • 45 D. 1 + x² + 12 1 + 360 .4 + .. 2x2 Е. 1 - 2! 2x4 2x6 4! 6! Enter your answer choice as "A", "B", "C", "D" or "E": ii.) Use the first 3 terms in the expansion in part (a.) to approximate 0.9 cos(2x) dx. Give your answer as a decimal value rounded to 6 decimal places. +
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