Find the flux of F¯ = (x − y)i + xj across the circle x 2 + y 2 = 4 in the xy-plane

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

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Q: Let F(x, y) = 3 i + j + 2k, and let S be a square whose side lengths are 3, parallel to the…

A: Flux is F.dA Where F is the Field and A is the area

Q: 3. Compute the scalar line integral 3 y – xz ds where C is the line seg- ment from (0, 1, 1) to…

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Q: Find the flux F(x, y, z) = (xy²,x²y, ln(x + y)) directed outwards through the surface of the solid…

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Q: Find the flow of F=xzi-yk through the upper part of plane z-1 in the x +y² +z = 4sphere. %3D

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

Q: 17. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: Let C be the parabola y = x² for 0 < x < 2. Let F(x, y) = ye"i + xe*"j.Compute the line integral

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y + 18z on the elipse…

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Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

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Q: Find the tangent plane for the level surface f(x,y,z) = 5x4 + cos (4y) + In (6z) = c at the point…

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Q: Determine the area that lies under f (x,y) = 9x² + 4xy + 4 and above the rectangle given by [-1,1] ×…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: If F= represents the flow of a liquid through a parabolic cylinder S: y=x, 0sxs2, 0szsl. That is…

A: If F→=y2,-x2,z2 represents the flow of a liquid through a parabolic cylinder S:y=x2,0≤x≤2,0≤z≤1.…

Q: Compute the flux of F = 3(x + z)i +j+3zk through the surface S given by y = x2 + z2, with 0 0, z >…

A: From given data we see that the surface is oriented towards xz plane,  Hence,  d→s=dxdzj→

Q: IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square…

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Q: 2. Show that f(t) =1 – sint defines a smooth flow on the manifold S = ( (cost,sint) ), but %3D g(t)…

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Q: Find the total differential of W = x^4 y^3 z^2 + x^3 Y^2 + x^2 z +y + 3 at (2,1,1)

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Q: Compute the line integral of the scalar function f(x,y,z)=2x2+8zf(x,y,z)=2x^2+8z over the curve…

A: To find the line integral, obtain dS as follows.

Q: 2. The task is to determine the flux of B across G, where G is the positively-oriented portion of…

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Q: 2). Find the flux of F(x, y, z) = (0, yz, z) outward through the surface S cut from the cylinder y +…

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Q: Calculate F - dS where F = (e² sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: Compute the flux of F = (5(z + 2), 5, 52) through the surface S given by y = ² + 2, with 0 0, z 2 0,…

A: We have to find flux.

Q: find the outward flux of F across the boundary of D.  F = 2xyi + 2yzj + 2xzk D: The cube cut from…

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Q: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 <y<9, x…

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Q: Use a parameterization to find the flux do of F = z²i+ xj – 4zk in the outward direction (normal…

A: Apply Divergence theorem to the given surface integral, ∬F.ndσ=∫∫∫DivFdV

Q: Find the potential function for F(x,y,z) = (x^-1z)i + (y^-1z)j + ln(xy)k. Show all steps and explain

A: Potential function of  F, is f such that ∇f=F.

Q: Suppose F = ∇ * A, where A = (y + sqrt(z))i + e^(xyz) j + cos(xz) k. Determine the flux of F outward…

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Q: Integrate G(x, y, z) = x - y - z over the portion of the plane x + y = 1 in the first octant between…

A: Given G(x,y,z)=x-y-z

Q: Compute the flux of F = (r, y, z*) across the cone z = x2 + y?, %3D 0<<1, in the downward direction.

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Q: (7) Determine the upward flux of ▼ × F through the part of the elliptical cone C = {(x, y, z)|z = 2…

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Q: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…

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Q: 5. Find the flux of F (x,y,z) = y cos(z)i-yx sin(x) j+ xy³k through the outward oriented cube of…

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Q: 2) Find the outward flux of F across the region D where F(x, y, z) = (In(x² + y²), –tan'(), zVx² +…

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Q: „ Compute the flux of F = xi + yj + zk through the curved surface of the cylinder x? + y² = 1…

A: Consider the vector field:

Q: 5. Find the flux of F = 2xi + (x- y)j across the circle r(t) = acos[t] i + asin[t]j,t e [0,2n]

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Q: Evaluate the solid bounded by 2x+z=2 and (x-1)2+y2=z.

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Q: 6. Compute the flux of F = [0, 0, z²] through the spherical surface S given as the upper hemisphere…

A: To find- Compute the flux of F→ = 0, 0, z2 through the spherical surface S given as the upper…

Q: find the flux of 3 – e")i+ (y³ + sin z)j+ (z³ – unded above by z = V4 – x² outward orientation.

A: We have to find the flux using the divergence therom according to the given information

Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y − 2) 2 = 2x − 2, S4: x = 0, S5:…

A: Consider the surfaces  S1: 2x + 3z = 6, S2: y = 2S3: (y − 2)2=2x − 2, S4: x = 0S5: y = 0S6: z = 0

Q: 5. Compute the flux of F(r, y.2) =zi- 2yj+ 2ak across the surface of the cylinder bounded by a+y =9…

A: Solve the problem as shown below.

Q: Integrate G(x, y, z) = x, over the parabolic cylinder y = x2, 0 &lt;=x&lt;= 2, 0&lt;=z&lt;=3.

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Q: 16. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: Find the flux of F(x,y,z) = (-x,-y, z³) , across S. Where S is the part of the cone z = /x² + y²…

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Q: (a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: Find the flux of F = (x - y)i + xj across the circle x2 + y2 = 1 in the xy-plane.

A: Given F = (x - y)i + xj  across circle x2+y2=1

Q: 2. Use the Divergence Theorem to calculate the flux of F(x, y, z) = (x³ + y) i+(y³ + 2³) j+(z³ + x²)…

A: The given vector field is  F(x, y, z) = (x³ + y) i+ (y³ + z³) j+(x³ + x²) k across the surface of…

Q: Find the tangent plane for the level surface f(x,y,z) = 6x3 + cos (4y) + In (4z) = c at the point…

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Q: 2. Show that f(t) = 1 – sint defines a smooth flow on the manifold S = ( (cost, sint) ), but g(t) =t…

A: The given question can be solved as shown in step2