Match each of the Maclaurin series with the function it represents. 00 x" 1. п! n=0 00 (-1)"x²n 2. (2n)! n=0 00 x2n+1 3. Σ-1", (2n + 1)! n=0 00 (-1)"x2n+1 4. 2n + 1 n=0 A. arctan(x) B. cos(x) C. sin(x) D. e*

Q: Find the nth coefficients of the formal power series 1. (Σπox") (Σo(−1)"x") 2. (Ση=ox") (Σποχη) n=0

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A: use this formula to get all the series

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A: We will use Taylor's series expansion to find resulting power series.

Q: Find the Maclaurin Series of the following functions. sin(x²) 2 sin(x) 3 arctan(x)

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Q: sin² n (2) Σ01 n=1 2n

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Suppose that the Fourier series for a periodic function f(x) on the interval (-1, ) is given as f(x)…

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