(-1)"x2" (2n)! +00 1. For all x ER, cos x = Σ n=0 a. Find a power series that is equal to x cos(x) for all x E R. b. Differentiate the series in item 1(a) to find a power series that is equal to cos(x²) – 2x sin(x²) for all x E R. +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b) to prove that ) = cos(4) - 8 sin(4). n=0
(-1)"x2" (2n)! +00 1. For all x ER, cos x = Σ n=0 a. Find a power series that is equal to x cos(x) for all x E R. b. Differentiate the series in item 1(a) to find a power series that is equal to cos(x²) – 2x sin(x²) for all x E R. +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b) to prove that ) = cos(4) - 8 sin(4). n=0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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For item 1, use theorems under Functions as Power series
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