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A: Find the Fourier Legendre series for the function e ^ (-x^2)

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Q: 1. Find ao, ak, and by the Fourier series of the function { f(x) = = -1<x<0 -x 0<x< 1

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A: The given vector fields are and .We need to plot sketch the vector fields in the plane.

Q: Show that the operator U is a partial isometry U: L² ([0,1]) → L² ([0,1]), Uƒ(x) = X[0,1] ƒ(x)

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Q: You Wrtie sqrt 29 in its continued fraction expansion.

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Q: Find the derivative d (et² + 3)s A.5(ex²+3)4.ex² B. 10x(ex+3)4 ex² 2 C.5(ex+3) 2 D. 10(ex²+3)4.ex² 2

A: We use power rule

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