39. Let S be the portion of the cylinder y = e* in the first octant that projects parallel to the x-axis onto the rectangle Ry: 1

Q: What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

A: We find the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

A:

Q: Consider the vector field v(x)

A: Given, the vector field        v(x)=yx2+y2i^-xx2+y2j^+6k^                               ...(1)

Q: = (4x° – 7y)i + (9y' + 7x – 7)j %3D - ndary of the parallelogram in the following figure (note the…

A: Introduction: Let D be associated open, a merely connected region with a piecewise swish,…

Q: Evaluate F dr, where C goes along the curve {x* + y* = 1, z = 2} from (1,0, 2) to (b) (0, 1, 2).

A:

Q: 3) Let S be a portion of the surface 3z = 12 – 6x – 3y in the first octant. Suppose that S is…

A: 3z=12-6x-3y divide by 3 z=4-2x-y ⇒2x+y+z=4 clearly it's plane The plane cuts the x-axis at (2,0,0),…

Q: Consider the vector field F(x,y,z) = (3x²y)i + (x³ + 1) + (92²) and the curve C made up of the…

A:

Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, 4)…

A: As per Bartleby guidelines I have authority to answer only one question. If you want other…

Q: Suppose the vector field v(x, y, z) = (4xy2, -4xz², 5x) represents the velocity field of a fluid.…

A:

Q: Consider the vector field F(x, Y, z) = 3x?yi+ (x³ + 1) j+9z²k. Let C be the circle cut from the…

A: Given vector field is  F(x,y,z)=3x2yi+(x3+1)j+9z2k C be circle cut from sphere x2+y2+z2=8 by the…

Q: Sketch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line…

A:

Q: Find the flux of the constant vector field =-7-j+ k through a square plate of area 25 in the…

A: A constant vector field  and a square plate of area 25 in the xy plane oriented in the positive z…

Q: Let C₁ be the line segment from the point (-4, 8) to the point (2, -4), C₂ be the arc on the…

A:

Q: Consider the vector field F = (2, -3). Let C be the straight line segment oriented from point (3,0)…

A: Given vector field, So,

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

A:

Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

A:

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: 12. Use a parameterization to find the flux across the surface cut from the cylinder x? + y? = 1 by…

A: Image is attached with detailed explanation.

Q: 1. Let F =i+y^2j +z^4k. Find the general flow lines for this vector field. Present the flow line…

A: Consider the provided question,

Q: 26. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y+z)k and surface z = 4x² - y², z ≥…

A: The given problem is to verify the stokes theorem for the given vector field over the given surface…

Q: 5) Find the flux of F = (-2y, -x) on the circle of radius 2 centered at the origin. Use the vector…

A: When the field vectors are going the same direction as the vectors normal to the surface, the flux…

Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

Q: Find the outward flux of the field F = 8xyi + 4yzj + 2xzk across the surface of the cube cut from…

A:

Q: Let f (x, y) be a harmonic function such that ∇f (1, 1) = (−1, −3). Show that the point P (1, 1) is…

A: To show that P(1,1) is a sink for the vector field G, we need to show that the vectors in the…

Q: 9. Find the flux of the vector field B(x, y,=) shown in the left figure through the square S of - yỉ…

A: The general form of a vector valued function in three dimensions is given by…

Q: Calculate the flux of the vector field F(x, y, z) = (3x + 5) through a disk of radius 4 centered at…

A: we use the formula Flux=∮F.ndS to calculate the flux.