Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z...

Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z + z^3 ) across the outward oriented faces of a cube without the front face at x = 2 and with vertices at (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

Expert Solution

milcah answered 2 years ago

Find the flux of the vector field F = x i + e2x j + z ...

Find the flux of the vector field F = x i + e2x j + z k through the surface S given by that portion of the plane 2x + y + 8z = 7 in the first octant, oriented upward.

Let F be a vector field. Find the flux of F through the given surface. Assume...

Let F be a vector field. Find the flux of F through the given surface. Assume the surface S is oriented upward. F = eyi + exj + 24yk; S that portion of the plane x + y + z = 6 in the first octant.

Find the flux of the vector field V(x, y, z) = 7xy2i + 2x2yj + z3k...

Find the flux of the vector field V(x, y, z) = 7xy2i + 2x2yj + z3k out of the unit sphere.

Calculate the flux of the vector field F? (r? )=9r? , where r? =?x,y,z?, through a...

Calculate the flux of the vector field F? (r? )=9r? , where r? =?x,y,z?, through a sphere of radius 4 centered at the origin, oriented outward. Flux =

Compute the flux of the vector field F = <xy, 5yz, 6zx> through the portion of...

Compute the flux of the vector field F = <xy, 5yz, 6zx> through the portion of the plane 3x + 2y + z = 6 in the first octant with the downward orientation.

Consider the vector field F(x, y) = <3 + 2xy, x2 − 3y 2> (b) Evaluate...

Consider the vector field F(x, y) = <3 + 2xy, x2 − 3y 2> (b) Evaluate integral (subscript c) F · dr, where C is the curve (e^t sin t, e^t cost) for 0 ≤ t ≤ π.

3. a) Consider the vector field F(x, y, z) = (2xy2 z, 2x 2 yz, x2...

3. a) Consider the vector field F(x, y, z) = (2xy2 z, 2x 2 yz, x2 y 2 ) and the curve r(t) = (sin t,sin t cost, cost) on the interval [ π 4 , 3π 4 ]. Calculate R C F · dr using the definition of the line integral. [5] b) Find a function f : R 3 → R so that F = ∇f. [5] c) Verify your answer from (a) using (b) and the Fundamental...

Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of...

Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of F across S, the top part of the paraboloid x2 + y2 + z = 2 that lies above the plane z = 1 and is oriented upward. Note that S is not a closed surface.

Use the extended divergence theorem to compute the total flux of the vector field F(x, y,...

Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x2 + 3xz − y, 2y3 − 6y, 9x2 + 4z2 − 3x outward from the region F that lies inside the sphere x2 + y2 + z2 = 25 and outside the solid cylinder x2 + y2 = 4 with top at z = 1 and bottom at z = −1.

Consider the following planes. 5x − 3y + z = 2, 3x + y − 5z...

Consider the following planes. 5x − 3y + z = 2, 3x + y − 5z = 4 (a) Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (x(t), y(t), z(t)) = (b) Find the angle between the planes. (Round your answer to one decimal place.)

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