For all x € R, sin.x = Σ (−1)"x2n+1 (2n +1)!* n=0 ■Find a power series that is equal to x³ sin(x²) for all x € R. ■ Differentiate the series in item 1(a) to find a power series that is equal to 3x² sin(x²)+2x* cos(x²) for all x € R. 3 Use the result in item 1(b) to prove that Σ (−1)ª(4n+5) 16″+1(2n +1)! = ³² sin (1) += cos (1).

For all x € R, sin.x = Σ (−1)"x2n+1 (2n +1)!* n=0 ■Find a power series that is equal to x³ sin(x²) for all x € R. ■ Differentiate the series in item 1(a) to find a power series that is equal to 3x² sin(x²)+2x* cos(x²) for all x € R. 3 Use the result in item 1(b) to prove that Σ (−1)ª(4n+5) 16″+1(2n +1)! = ³² sin (1) += cos (1).

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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