(-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
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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![ఆ (-1)"xW
1. For all x ER, cos x =
Σ
(2n)!
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) – 2x² 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5081a7d7-1f2c-48e2-81b7-8ab669831688%2F5a12a15a-27ef-4ddc-8d74-e901481849c1%2F9wq2ibv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ఆ (-1)"xW
1. For all x ER, cos x =
Σ
(2n)!
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) – 2x² 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
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