2. Verify that each given function u is harmonic (in the region where it is defined), then find a harmonic conjugate of u and the analytic function f(z) whose real part is u: (a) u = y u = e sin y u = xy = x + y

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A: Here we use definition of existence of limit to check  f(z) is continuous or not.

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A: Solution

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A: Determine the coordinates of the absolute extremes of y = 3sinx(cosx), 0 ≤ x ≤ 2pi

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Q: 9: Check Euler's Theorem for the Function

A: We checked Euler's theorem for function.

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A: Let  fθ=sin θ+cos θ Differentiate with respect to 'θ', we get f'θ=cos θ-sin θ For maxima or minima,…

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Q: A. Verify Clairaut's Theorem for the given function: F(U,W) = Sin(UW)- 4U?w2 %3!

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: We want to define A x B

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A: The given function is .The objective is to find the domain of the function and sketch the domain.

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