(-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
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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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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