Consider the gradient vector field V = Vg of the function g(x, y) = x² + y² + e*²-y´ cos(2xy). Compute the outward flux V. nds across the ellipse & = {4(x – 3)² + 9(y – 1)² = 1}. - -

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+e'cos (y)) j through the right…

A: Given vector field is F=  x2y + ex siny  i + x2 + ex cosy j Curve r2=cos2θ

Q: 4. Find the positively oriented flux over the surface created by the paraboloid z = 16 – x² – y2…

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Q: Find the counterclockwise circulation and outward flux of the field F = xyi + 4yʻj around and over…

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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: Consider the vector field F(x, y,z)= 2.xy i+(x² +z² ) j+2yzk. c) Is F a conservative vector field?…

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Q: Find the gradient vector field of f(x, y, z) = 9x² + 8y* + 6z3

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Q: ) Compute the flux of the vector field F = 5xi + 2yj through the cylindrical surface shown below, if…

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Q: If F (x, y) = x2 i + y2 j is a conservative vector field, find its potential function. With the…

A: The solution are next step is

Q: Find the outward flux of the given field across the given cardioid. 5x i+ (e*+5 tan 1ly)j 1 + y2 F =…

A: The following formula from Green's theorem is used to find the outward flux, outwards flux=∮F·n…

Q: Find the flux of the field F = y2i + xzj - k outward (normal away from the z-axis) through the cone…

A: Definition:

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: Consider again 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 gradient vector field of f(x, y, z) = e3r + 8y+6z

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Q: Find the potential function f for the CONservative vector field 言こ<2xe' x2+y? 2ge %3D fCx,y) e 2.…

A: The complete question is solved in next step

Q: Find the gradient vector field of f(x, y) = tan(2x − 3y).

A: Given fx,y =tan2x-3y         we find the gradient vector of fx,y

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: The circuitation of the vector field F(x, y)- (3 + xy´, 4x + xy) along the boundary of the plane…

A: The solution are next step

Q: Find the gradient vector field of f(x, y, z) 5x+ 2y+8z

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

A: Given a field: F=x2i+y2j We need to find the flux of this field across a closed plane curve C which…

Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = Jx2 + y2 + 3 that…

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Q: Calculate the flux of the vector field (x, y³), out of the annular region between the x? + y? = 1…

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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: Find a potential function for the conservative vector field. F(x, y) = xex*4Y(2yi + xj)

A: If curl f is zero then conservative field

Q: Evaluate the outward flux of the vector field F = (2x² – 5e" + sin(z²), –4ry + In(x*), 5z – 3x²y®)…

A: We can see that the region given here is closed, so…

Q: Determine whether the vector field…

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Q: 2的 在年

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Q: Given a scalar function V(x, y) =-(x² +y² ), the directional derivative of V in the direction of the…

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Q: Calculate the flux of the vector field F = -2i + 5æ²j – 3k, through the square of side 2 in the…

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Q: Find the gradient vector field (F(r, Y, 2)) of f(x, y, z) = In(4x + 6y + 22) . F(7, y, 2) = (

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Q: (a) Compute the flux of the field F = r i+yj-zk across the cylindrical surface a + z = 1, 0 <y53…

A: If E be a  solid region bounded by surface of S with positive orientation then for a vector field…

Q: For Problem 2, calculate the flux of the vector field F through the given surface S. 2. F = -4i+…

A: Given F→=-4i^+xj^+2zk^ and S:x+2y+z-2=0

Q: For what values of a and d does the vector field F = ⟨ax, dy⟩ have zero flux across the unit circle…

A: A vector field, have zero flux. Across the unit-circle centered at the origin and oriented…

Q: Compute the flux

A: Compute the flux

Q: Find g(x, z) so that F(x, y,z) = (8x cos y sin? z + 2e2xz)î – (4x² sin y sin? z)j+ (g(x, z) cos y +…

A: Given that    Fx,y,z=8x cosy sin2z+2e2xz i^-4x2 siny sin2z j^+gx,zcosy+2e2xz k^ Now we have to find…

Q: Find the gradient vector fields for the following potential functions (a) f(x,y) = x²y – xy?

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Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

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Q: Find the outward flux of the given field across the given cardioid. F=(3ry-)i+(e* +5tan-y)j 1+…

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Q: Find the work done by the force field F(x, y) = xi + 2yj on a particle moving along the path C:x =…

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Q: Determine the gradient of the give scalar field V = e(2*+3y) cos 5z at R(-0.1, 0.2, 0.4).

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Q: Find the flux out of the curve bounded by the top half of = arccos(√√²+² ) and y=0 with vector field…

A: As per the question we are given a bounded curve C and a 2d vector field F And we have to find the…

Q: Consider the surface integral of the vector field F= [xy², 3x², x²z]over a surface S, where S…

A: From Gauss divergence theorem, we have ∬SF→⋅dS=∭VdivF→dV   The vector field is F→=xy2,3x2,x2z.…

Q: If F = (4xy – z³) î + 2x² ĵ – 3xz² k is a conservative force field, then scalar potential of F is…

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Q: Find the potential function for the following vector field F(x, y, z) = (2x cos y – 2z3) î + (29+…

A: F = &lt;2xcosy-2z3, 29+2ye2-x2siny, y2e2-6xz&gt; To check F¯ is conservative  not we have t check…

Q: Find the outward flux of the given field across the given cardioid. '=(3xy-1)i+(e²+5tan-'y)j 1+y…

A: Given the given expression is F=3xy-5x1+y2i+ex+5tan-1yjr=a1+cosθ, a≥0 Apply Green's theorem. Outward…

Q: For the force field F = (2xe¬Y, (2y – x²e¬y)) in some open connected region containing P(1, 0) and…

A: Given that, F=2xe-y, 2y-x2e-y If F is conservative then ∂2F∂x∂y-∂2F∂y∂x=0

Q: Find the counterclockwise circulation and outward flux of the field F = 7xyi + -5y²j C enclosed by…

A: Introduction: Let C be a piecewise smooth, simple closed curve enclosing a region R in the plane.…

Q: Find the flux of the field F = z k across the portion of the sphere x2 + y2 + z2 = a2 in the first…

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Q: Find the gradient vector field of f(x, y, z) = e® 5x+2y+8z

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Q: Find the outward flux of the given field across the given cardioid. F=(3ry-)i+(e*+5tan-'y)j 1+y?…

A: The outward flux of given field is given by using greens theorem.

Q: Compute the flux of the vector field F = 2xi + 3yj through the cylindrical surface shown below, if a…

A: We have to compute the flux of the  given vector field.