Let F(x, y) = (4 cos(y), 2 sin(y)). Compute the flux $ F - n ds of F across the boundary of the rectangle 0< x < 5,0 < y < using the vector form of Green's Theorem. (Use symbolic notation and fractions where needed.) nds = Incorrect

Q: 6. Find the flux of F (x,y, z) = y cos(z) i – y x sin(x)j+xy³k through the outward oriented cube of…

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

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Q: Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface…

A: Here we will use Stokes theorem  to calculate  flux of curl (F) on surface S bounded by curve C…

Q: Find the curl of the vector field F(x, y, z) = e" sin yi – e" cos yj O -2e" cos yk O -2e" cos y O…

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Q: 9. Compute the flux of the vector field F(x, y) = (-x sin(1+xy) – 4 cos(TY), y sin(1+ xy) + 6x)…

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Q: (b) Compute the flux of the vector field F(x, y, z) = y i– 2.xyk over the triangle T with vertices…

A: Given vector field is: F→=yi^-2xyk^ Given vertices of the triangle are: 1,0,0, 0,1,0 and 0,0,2 Then…

Q: Calculate the work done by the force field F (x, y) = (x ^ 2, ye ^ x) on a particle that moves along…

A: Given:

Q: 1) Consider the closed surface: z = h – x^2 – y^2, h>0, and z=0. Let F=(x^2,y^2,z^2). Find the flux…

A: Consider the given information: The given surface is  z=h-x2-y2,     h&gt;0z=0 Also F→=x2, y2, z2 To…

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = tan(6r + 2y + 2) . F(2, y, 2) =

A: Find the gradient vector field

Q: 1. Consider the vector field F(x, y, z) = (2e2" cos(3y), –3e²" sin(3y) + Y a. Find divF(x, y, z) and…

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Q: Find the flux of the field F =(x + y)i -(x2+y2)j outward across the triangle with vertices (1, 0),…

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Q: Find the flux of F = yi + 2zxj – z²k through the parabolic cylinder y = x2,0 < x < 1,0 < z< 4, in…

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Q: Find the outward flux of the field F = 8xyi + 6yzj + 6xzk across the surface of the cube cut from…

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Q: 4. Find the work done by the force field F = (x? sin(y),y) on a particle that moves along the cubic…

A: Given: The force field, F→=x2siny,y on a particle that moves along the cubic y=x3 from 1,1 to 2,8.

Q: Consider the vector field F = = (x + y)i+ (x² + y² )j. What is the downward flux across the line…

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Q: Find the circulation and flux for the field F(x, y) = (y – 6x² , x+y²) around and across the…

A: Given data field Fx,y=y-6x2,x+y2 around and across the triangle given by y=0, y=x and x=1.

Q: 2) Given the vector field F = (- Vx²+y² 2z2) write the integral to calculate the outward x²+y² flux…

A: We have to find the outward flux across the cylinder x2+y2=100.

Q: | 23. Find the outward flux of the field F = ( 3xy i + (e* + tan¯ly)j х 1 + y?, across the cardioid…

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Q: 23. Find the outward flux of the field i + (e + tan'y)j 1 + y², F 3xy %3D across the cardioid r =…

A: Given: The following formula is used to find the outward flux, Comparing with the general form,…

Q: 10. [ Find the flux of the vector field F(x, y, z)= 3 over the surface S, where S is the surface of…

A: The general form of a vector-valued function in three dimensions is given by F→=Fx, Fy, Fz, where…

Q: (b) For the case a = 3, b = 4, and for the constant vector field F(x,y,z) = 4 1 + k , find the flux…

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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: Let F =. Find the flux F n ds, where C is the boundary, taken counterclockwise, of the rectangular…

A: Given function is F=xy, x2y                   (1) Since we know that, for function F=P, Q, the flux…

Q: (c) Determine the flux of the vector field F = x³i – 2yĵ + 7z²k across a cone z = x2 + y2 + 3 that…

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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: Compute the flux ∮∂D F • n ds of F(x, y) = {x3, yx2) across the unit square D using the Flux Form of…

A: Given the equation F(x, y) = (x3, yx2)  The closed surface is the unit square the limits of x and  y…

Q: 2x Find the gradient vector field (F(, y, z)) of f(x, y, z) = y cos F(2,y, 2) =

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Q: Find the work done by the force field F(x, y) = x sin y i + y j on a particle that moves along the…

A: Explanation: Given that,  Force F and a parabola from (-1,1) to (2,4)…

Q: Find a potential function for the vector field F(x, y) = (6x sin y, 3 cos x ), if it exists. A. No…

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Q: Find line integral fF. dr of conservative vector field F (x, y, z) = 'i+ j+-k where C is a path from…

A: Find the line integral of a conservative vector field

Q: Find the work done by the force field F(x, y) = x sin(y)i + yj on a particle that moves along the…

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Q: Find the total flux of the field x+ /1+ y² + z² 2y + V1+x²+ z² \3z + /1+x² + y², F(x,y, z) = out of…

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Q: Find the work done by the force field F(x, y) = x sin y1 + y J on a particle that moves along the…

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Q: I have trouble getting to the answer. Just wondering if I can get it step by step.

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Q: The work done in moving a particle in the force field F= x- i+ 3xy j from (0,0) to (1,2) along the…

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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: Given the radial field (x, y, z) (x² + y² + z²)³/2 |r|3/2 Find the outward flux across the sphere of…

A: Image is attached with detailed solution.

Q: Calculate the flux of the field F=xi+yj across the closed plane curve C, where C is the closed…

A: theory: graph:

Q: Let F(x, y) = (5 cos(y), 8 sin(y)). Compute the flux F nds of F across the boundary of the rectangle…

A: Let F(x,y)=5cos(y),8sin(y),To compute the flux ∮F.n ds of F across the boundary of the rectangle…

Q: Show that the function f(x, y) = In /x² + y² satisfies the Laplace equation. %3D

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Q: yz Find the flux of the field F up through the part of the 1+ xy, paraboloid z = 1 - x² – y² that…

A: Given field F=yzxz1+xy  The part of the paraboloid z=1-x2-y2 cut off by the xy-plane with upward.…

Q: Find the flux of the fields F1 = 2x i - 3y j and F2 = 2x i + (x - y)j across the circle r(t) = (a…

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Q: If f(x,y)=x2+y², then the gradient field at (1,-1) is given by: O. f(x,y)= -2i + 2j O II. f(x,y)=…

A:

Q: Find the flux of the curl of the vector field F(x, y, z) = [(z2 −4) cos(xyz), 3x+y,(z2 −4) sin(ex…

A: Surface is oriented outwards. And -2 &lt;= z &lt;= 2

Q: Find the flux of F = (3z + 1)k upward across the hemisphere x2 + y2 + z2 = a2, z&gt;= 0 (a) with the…

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Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

A: Flux of the given field is given by

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: Calculate the flux of the field F across the closed plane curve C. F=xi+yj, the curve C is the…

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Q: 1. Find the work done by the gradient of f (r. y) = (r+ y)? counterclockwise around the circle 2+ y?…

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Q: Find the flow of the velocity field F = b. a. Na g (2,8) : 4x (0,0) X (5y² + 1)i + (10xy)j along…

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.