Find the gradient of the following scalar fields: a) F=x^2+y^2 b) V=p^3z cos2phi

Q: A quarter cylinder of radius 2 and height 5 exists as shown in the figure below. Surface integral of…

A: Given that the quarter cylinder is of radius 2 and height 5. This means that the radical distance…

Q: The gradient of a scalar field V is a vector that represents both magnitude and the direction of the…

A: Given : The gradient of a scaler field V is a vector that represents both magnitude and direction…

Q: Find the gradient vector field for the scalar function f(x,y)=sin(2x)cos(6y).   Enter the exact…

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Q: Find the conservative vector field for the potential function by finding its gradient.

A: Gradient for function h is given by , where are the partial derivatives. Partial derivative…

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: 9) Check whether the vector field F = (-cos x cos y, sin x sin y, - sec² z) is a gradient vector…

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Q: When is the vector field continuous?

A: given,       Continuous vector field .

Q: Show that the outward flux of a constant vector field across any closed surface to which the…

A: We have to Show that the outward flux of a constant vector field across any closed surface to which…

Q: Compute the curl of the following vector field. F = = (3z2 sin y, 3xz2 cos y, 6xz sin y)

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Q: Find the flux through through the boundary of the rectangle 0 < x < 6, 0 < y < 5 for fluid flowing…

A: Given F→=x5+y  , y cos3x flux=∫cF→.n^  ds =∫∫Ddiv F dA

Q: Find the gradient vector field of f(x, y) = ln(5x + y)

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Q: Find the gradient vector field of f(r, y) = In(x + 3y)

A: Solve for the gradient vector

Q: Find the conservative vector field for the potential function h(x,y,z)=3xyln(x+y) by finding its…

A: Find gradient

Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 3| for fluid flowing…

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Q: Find the gradient vector field of f(x,y) = x2 + y2 and sketch it.

A: Solution

Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

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Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…

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Q: Find the conservative vector field for the potential function by finding its F(x, y) = x² + 5y2

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Q: Sketch a few representative vectors of vector field F = ⟨0, 1⟩along the line y = 2.

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Q: Find the conservative vector field for the potential function by finding its gradient. g (x, y, 2) =…

A: We need to find conservative vector field.

Q: Find the gradient vector field Vf of f. 1 f(r, y) = (y – 2)?

A: For a given vector fx, y the gradient vector denoted by ∇f is ∂ ∂ xf∂ ∂ yfSo,=∂ ∂ x12y-x2∂ ∂…

Q: Show that the vector field F = x²i + (2yz)j+ y² k is conservative and then find the corresponding…

A: A vector field F is conservative if curl(F)=0 or ∇×F=0 The potential function is given by f such…

Q: Explain why a potential function for a conservative vector field is determined up to an additive…

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Q: Show that the vector field F=2xyi +(x -2y)j is conservative and evaluate the line integral |F•ds…

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Q: The work done by a force field in a moving particle around a closed path is zero.

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Q: compute dr for the vector field where Cis the line segment from Co.o) to Cli3)

A: Given vector field is, F=1+x2,xy2  The objective is to compute ∫CF·dr, where C is the line segment…

Q: Calculate the divergence of the scalar field F(x,y)=3x2+siny.

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Q: 6. What is the corresponding vector fieldV for the scalar potential p(x, y)= In(x+ ¥)?

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Q: Find potential 9, for the conservati ve field the vector F (x, y,a)- (2xe? - y*sinx) î * sinx) î +…

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Q: Calculate the line integral of the vector field F = -3 i+ 2j along the line from the point (4, 0) to…

A: To find the line vector of following vector fieldF→=-3i+2jalong the line 4,0 and 12, 0

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: Given: f(x, y, z) = 9x2 − xy − z2

Q: Calculate the line integral of the vector field F = -2i+ 4jalong the line from the point (3,0) to…

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Q: Find the flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: Determine the gradient of the give scalar field V = e(2*+3y) cos 5z at R(-0.1, 0.2, 0.4).

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Q: Let W be the region between the sphere of radius 4 and the cube of side 1, both centered at the…

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Q: Consider the vector field F = ⟨ 1 , y ⟩ .Compute the path integral of this field along the path:…

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Q: A=(2x-3y)ax+(2xy-y2)ay Prove the Stokes theorem for the triangular linear path in the shape that is…

A: The general form of a vector valued function in a plane is given by A=Axax+Ayay, where Ax and Ay are…

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: Given : f(x,y,z)=9x2y+5z2   To Find : Conservative Vector field by finding it's gradient

Q: Find the gradient vector field of f(x, y) = x° sin(9y). F(x, y) = x°i+ sin(9y)j F(x, y) = 9x°…

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Q: Prove that F = (y' cosx+z')î +(2ysin x-4)ĵ+(3xz² +2)k is a conservative force field, find its scalar…

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Q: Show that the vector field F = 2xyi +(x² - 2y)j is conservative and evaluate the line integral (F•dš…

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Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

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Q: If the vector field A = âx3x² + âyy – â̟5z³ is given, express à in cylindrical and spherical…

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Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A: We have to find the conservative vector field.

Q: Find the gradient vector field of f(x, y) = In(2x + 3y) V

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Q: The necessary and sufficient condition that a velocity potential exists is that curl of V is…

A: We have to solve given problem:

Q: Find the gradieat of the functionf = xyz-4y2z. Visualize the vector field of the gradient. %3D

A: In vector calculus, the gradient of scalar valued function denotes the direction in which the…

Q: Compute the divergence and curl of the vector field cos (22 ) sin² (z² yz) 10 yz4 – xyz2 at the…

A: We have to find divergence and curl of vector field:

Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…

Q: Express the vector field D = ( x2 + y2 )-1 ( xax + yay ) in cylindrical components and cylindrical…

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