Considere o campo F(1, y) = (–2y+2z², –4z – 2y²) definido em todo o plano R?. Seja C C R² uma curva simples fechada (orientada no sentido anti-horario) delimitando uma região RC R? cuja area é . Determine fe F - dř. Escolha uma opção: 글 а. b. -2 c. d. e.

Q: For the vector field F(x,y) =(2xy²+2y)-i+(2x²y+2x)•j a) show that_F_is conservative vector field; b)…

A: Vector field and integration

Q: Let F be the following vector field: F(x,y,z) =. A. Find div F B. Show that there is no vector field…

A: Given: Fx, y, z=e-x siny, e-ysinz, e-zsinx (A) To find: Div F. (B) To Show there is no vector G such…

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Q: Explain Divergence of curl of B.

A: Let f = f1i+f2j+f3k Then curl(f) is given by ∇×f = ijk∂∂x∂∂y∂∂zf1f2f3=…

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A: U=exyax+sinxyay+cos2xzaz

Q: - Find the divergence and the curl of the vector fields A = xz³i - 2x²yzj + 2yz¹k B = x²yi - 2xzj +…

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Q: Define Vector Line Integral.

A: A line integral is the integral of some function along a curve. One can integrate a scalar-valued…

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Q: Let F = (x^2 + y^2, x^2 + y^2) be a vector field and C be the simple closed curve given by circles…

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Q: 2) For the vector field F(x, y, z)=(xz²-x²y)i + (xy²-y³2²)] +xy²z³k, find the following: a) Find the…

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Q: F be a vector field on R^3 whose components are differentiable. Show that ∇·(∇×F) = 0.

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Q: Determine whether →F(x,y,z)=3x^2yˆi−yzˆj+zx^2ˆk is a conservative vector field.     Component of…

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Q: 7) Consider a vector field F(x, y, z) = 3yi − xz j + yz².k. Let S be an equation of 2z = x²+y²…

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Q: Find the work done by the vector field F =( y+x 2, 2%y+z, 2yz + 2) %3D the Curve C ( all over it)…

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Q: 3) Determine whether or not the following 3D vector fields are conservative: a) (y²-z³)i + (2xy +…

A: As per the company rules we are supposed to answer only the first question and rest can be reposted.

Q: The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In…

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Q: of f. Sketch the gradient field for f (x, y) = /x² + y? along with several level curves

A: Here we have,

Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

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Q: Can you find a vector field whose curl is z?i? What about x2i? Explain your answer.

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Q: Let f : R2 → R with f(x,y) = px^2 + y^2. Sketch the graph of f. Prove that f is not differentiable at…

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Q: a 3d vector field given by V=5xyi+5yj-4zk represents the flow of water out of a system. use gausses…

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Q: Apply fundamental theorem for conservative vector field to find the line integral fF dr where F =…

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Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

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Q: Let ryz , (교2 + y"), 17 F = ( x2 +y? be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}.…

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Q: Exercise 5.4.2. Find the upper sum and lower sum for each of the following functions with respect to…

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Q: The magnetic field B due to a small current loop (which is placed at the origin) is called a…

A: Let S be a surface enclosed by the curve C , then ∬ScurlF→⋅dS→=∫CF→⋅dc→

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Q: True or False: Let F(x, y) be an incompressible vector field for which div(F) = 0. Let C be the…

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…