Compute the divergence of the vector field F(r, y, z) = (5x + 12ry)i+ (y + e" sin z)j + (5z + e" cos z)k at the point (2,0, 1). div(F)= Your answer should be an integer. Give a numerical answer only.

Q: Compute the upward flux of the vector field Ĥ(x, y, z) = (x, 0, 2z) across the portion of the…

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Q: Compute the curl and divergence of the vector field F(x, y, z) = (T 2², 2yz) . Is F conservative? If…

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Q: Compute the work done by the vector field F(x, y, z) = (,2, 2yz) when moving a particle: 1+? > a)…

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Q: Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, –6z – 32²y²)…

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz2j + 4yz²k; (5,…

A: Recall divergence is a scalar and has formula enclosed in next page

Q: F = (x² +y², y² +z?,.

A: on solving this we get the

Q: Consider vector field: F = e i-cos y j+ sin² z k. Obtain divergence and curl for F at points (0,,).

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Q: Find the work done by vector field F(x, y, z) = xi + 9xyj - (x + z)k on a particle moving along a…

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Q: Determine whether the vector field F(x,y,z)=(y,x,1) is conservative on R° . If so, determine a…

A: Given the vector field Fx,y,z=y,x,1=yi→+xj→+k→.

Q: Calculate the divergence of the vector field. F(x, y) = 3x°i – 2x sin(xy)j div(F) =

A: Given vector function F(x,y)=3X3 i -2x sin(xy) j divF=i∂∂x+j∂∂y+k∂∂z.F

Q: Compute the flux of the integral of the vector field F(z,y, 2) = (2,y, 2) through the half cylinder…

A: Given vector field is, Fx,y,z=x,y,z. It can be written as,  Fx,y,z=xi^+yj^+zk^. Flux of vector field…

Q: Find the work done by the vector field F = in moving a particle around the circle x2 +y2 = 4 from…

A: The given vector field is F=x-y, xy. The particle is moving around the circle x2+y2=4 from 2,0 to…

Q: 3 , find a potential function for the vector field F by inspection or show that one does not exist.…

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Q: Find the conservative vector field for the potential function by finding its gradient. (x, у, 2) %3…

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Q: Show that the vector field F = 2xyi + (x - 2 y)j is conservative and evaluate the line integral %3D…

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Q: 2. Show that V(V × F) = 0, here vector field is twice differentiable. %3D

A: This question is from vectors.

Q: Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) .   Enter…

A: The given vector field is : Fx,y,z=xyzi-yzj+xzk To find the divergence at 8,3,2

Q: Find the divergence of the vector field F = < ya®, æ2®, zy* div F = Preview

A: Divergence of F→=yx3, xz6, zy4

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, a) + (2y-3')] + 7k…

A: Solution :

Q: Verify the Divergence Theorem in the calculation of the flux of the vector field: through the…

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

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Q: Calculate the work done by the vector field F(x, y)= ,2xy) on a particle that moves once around the…

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Q: Consider the vector field F(x, y, z) = (ycosh x + ze*, sinh x – 3z³, e* – 9yz²) a. Find the…

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Q: Find the divergence of the vector field. V(x, y, z) = 4yzi + 6xzj + xyk div(V) =

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Q: Graph the vector field F(x, y)=(-3y, 2x); also find the divergence and the rotational.

A: The graph of the  vector field F=-3y, 2x is as follows

Q: Find a potential functioon for the conservative vector field given by y3/2 3 xy + z, 2 sin z 2.x…

A: According to question,Given vector field,F→x, y, z = 2xx2 + cos z-y322x, -32xy+z, -sin zx2 + cos z+y

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

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

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

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Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

Q: Compute the flux of the vector field F = xi + yj through the surface S, which is the part of the…

A: Given: F→=xi→+yj→ z=36-x2+y2 ds=1+∂z∂x2+∂z∂y2dxdy       =1+4x2+4y2dxdy   and…

Q: Find the divergence of the vector field F = < ya", xz°, zy* div F

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Q: Calculate the divergence of the vector field F (x, y, z)

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Q: Compute the flux of the vector field F(x, y, z) = 3x + 3yk through the surface S, where S is the…

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Q: Show that the vector field =(-2 x²y xy²¹ is conservative by finding all its potential functions.…

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Q: Compute the work done by the vector field F(x, y) = (ry, x² + y³) when moving a particle…

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Q: The divergence of the vector field F(z, y, z) = (ya°, az", zy?) is: %3D

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Q: 3. Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, -6z –…

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Q: Find the divergence of the vector field F. F(x, y, z) = In 5x²+ + 10xyj + In( 2y2 + 722)k div F(x,…

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Q: Show that the vector field F(x, y, 2) = (2x cos y – 3)i – (x² sin y + 2²)j – (2yz – 2)kis a…

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Q: Find the divergence of the vector field F = < yx², xz", zy® div F II

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Q: 6) Given the vector field F = (-x,-y,-z) '(x²+y2+z²)3/2! write the integral to calculate the outward…

A: First we parameterize field F then we calculate the Flux across the sphere using following formula:

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 4yz²k; (3,…

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Q: 3. Use the divergence of the vector field to compute F(x, y) = (tan-1 (2x)) ₁ + (xy-2 +²8²) J j 4 fo…

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Q: Compute the outward flux of the vector field F = (5xy, 5y²) for the region enclosed by the curves y…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Use the divergence of the vector field to compute F(x, y) У · (tan-¹ (2x))i + (xy − 2 + 8x²) j - = 4…

A: we are given the vector field as  F(x,y)=tan-1(2x)4i+(xy-y2+8x2)j to compute…

Q: Consider a conservative vector field: F(x, y) = (y cosx + y2, sinx + 2xy – 2y) Find a potential…

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Q: Suppose a vector field F(x, y) = wai + VEj is conservative. Then construct a potential function ø(x,…

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Q: Q3 Show that the vector field F= 2xyi +(x -2y)j is conservative and evaluate the line integral |F•ds…

A: Solution

Q: B) Find the work done by the conservative vector field F (x, y, z) = yzi+xzj+xyk along a smooth…

A: Since, it is given that the field is conservative.