Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. a. f(x)=1,a= b. f(x)=lnx, a=1 2 c. f(x)=cos²x, a=0.

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A: Here we have to verify the Green's theorem.

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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A: Given,            f=1x2+y2+z2To find : ∇f