4)Find the scalar function ø such that F = V ø where F=- y * +y x +y

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A: This is a problem of vector calculus.

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Q: (4)Find the scalar function such that F = V ø y i+ where F=- *+y x+y

A: We can find scalar function ϕ such that F→=∇ϕ ;where ∇ =i^∂∂x+j^∂∂y+k^∂∂z

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Q: a) Find a scalar function f such that F= Vf where F(x,y) = (3 + 2xy²) i +(2x²y)j.

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

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Q: Exercise 5 3x + ax + b x² +1 Conşider the function f that is defined over IR as: f(x) = Where a and…

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Q: 2. (a) Prove that the function f(x, y) = xy is differentiable everywhere in its do- %3D x² + y?…

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Q: Determine if the function satisfy the Cauchy-Riemann equations. 5. f(z) = z?

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Q: 2 find holomorphic function f(z) = u(x, y) + jv(x, y) if  v(x, y) = 2*x*y + 3*x f(0) = 0

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Q: 5sqrt(x^2 + y^2).

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Q: (d) Let y and be scalar fields. Prove that V (Vy x V) = 0. (e) R=xi + yj + zk and let r = Prove that…

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