The value of a' for which f : R → R, ax +7 flx) is invertible lies in %3D 2 x* +4 (а) (0, 2) (b) (1, ое) (c) (0, 0) (d) none of these

Q: Determine the divergence of vector field E = 3x²x + 2zŷ + x²z2 at (2, –4, 0).

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Q: Find the divergence of the field. F = (2x+7y-8z)i + (5x +3y+6z)j + (-6x-y+2z)H div F =

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Q: 0 0 0 1 0 0 0 1 0 ) Let A =

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Q: Find the gradient vector field for the scalar function f(x,y)=sin(2x)cos(6y).   Enter the exact…

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Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F 3D6xi+ 6уј+ 6z k;…

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Q: b) Show the force field M UTM UTM F(r, y, z) = (r²y + In(yz)) i+ UTM 3 + y cos(2z) ) j+ tial…

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Q: Derive a Dirichlet principle for the elliptic operator L in divergence form with A e C² and b= 0.

A: Given elliptical operator L~ in divergence form with A∈C1 and b=0. Suppose A∈C1Ω of the second order…

Q: Consider the subspace W of D, given by W = span(sin x, cos x).                         (a) Show that…

A: Given Subspace W=span(sin x, cos x) of D{space of all differentiable functions} B={sin x, cos x}

Q: The result from the preliminary method of coefficients linear with two variables is what type of DE?…

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Q: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

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Q: Find the conservative vector field for the potential function by finding its gradient. (x, у, 2) %3…

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Q: 4. Suppose that an insect population, z(t), is controlled by a natural predator population, y(t). a)…

A: Since the sub parts are not specified so i am solving first three parts. (a) It is given that an…

Q: 5. Compute div F and curl F if F = (2x – cos y)i – x²e32j + (z² – 7x)k. 6. Determine if the vector…

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Q: 2. Show that V(V × F) = 0, here vector field is twice differentiable. %3D

A: This question is from vectors.

Q: Compute the flux of the vector field (x, - xy*), out of the rectangle with vertices (0,0), (5,0),…

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Q: Find the divergence of the field. F= (4x + 5y + 7z)i + (8x - 8y + 3z)j + (2x - 7y + 4z)k div F =

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Q: 4. Find the flow of the velocity field F = V(xy²z³) along the line segment from (1,1,1) to (2,1,…

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Q: Show that the force F = (y^²2² - 6xz² ) ₁² + ²xyz²³ j^² + (3 xy² z ²-6x²²Z) k IS Conservative, hence…

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Q: Find the conservative vector field for the potential function by finding its gradient. g (x, y, 2) =…

A: We need to find conservative vector field.

Q: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…

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Q: please explain this solution (orthogonal projection onto W) 1 1 1 1 1 1 1 0 0 1

A: Given: To explain the given solution as follows,

Q: A scalar field is given by f = x2/3 + y2/3, where x and y are the Cartesian coordinates. The…

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Q: 3. Verify that the vector X is a solution of the given linear system. dx = -x – 2y dt cos 4t – sin…

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Q: In R°, the Klein-Gordon equation governs the quantum mechanical wavefunction (r) of a relativistic…

A: Suppose, for a given set of boundary conditions  ψ=for we have ∂ψ∂n=g on S we have two solutions to…

Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x F(x, y) = -

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Q: Show that the vector field F = (yz² ye, rz² - e, 2xyz) is conservative, and find a potential…

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Q: Find a potential functioon for the conservative vector field given by y3/2 3 xy + z, 2 sin z 2.x…

A: According to question,Given vector field,F→x, y, z = 2xx2 + cos z-y322x, -32xy+z, -sin zx2 + cos z+y

Q: .) Find the work done by field F = (-y,-x) along curve C: counter clockwise along semicircle y = v4…

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Q: 1. Use isoclines to sketch the direction field for y' = x+ 2y and sketch the solution curve that…

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Q: 2. Use the Fourier transform to solve this transport equation for u = u(x, t), defined on the whole…

A: Given that                       2ut-3ux = 0 and  u (x,0) = e-x2            We can write this as…

Q: Vector Field F = 6xi + (2y – y²)j+(6z – x³)k is Conservative Select one: True False

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Q: 10. Integral 2-t dt

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Q: (2) Find the line integral of the vector field F(x, y) = (-1,3) along the path from (2, 3) to (2,…

A: The vector field F→=-1, 3To find line integral of vector field along the path 2, 3 to 2, 5

Q: Show that the vector field =(-2 x²y xy²¹ is conservative by finding all its potential functions.…

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Q: If. E-Pi+Q+Rk is.a.veeter field.and. Po.Q.and R. have.centineons. 2nd order.partial.derivatives.then…

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Q: Express the field D = (x2 + y)-(xax + yay) in cylindrical components

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Q: Compute the flux of the vector field (x3, – xy³), - out of the rectangle with vertices (0,0), (3,0),…

A: Given: F=x3 ,-xy5with rectangle with vertices (0,0) , (3,0) , (3 ,2) , (0,2) To find flux of vector…

Q: 11) → 2 center : (2, 1), k= Ay tコーt-tt rt-FナーFナ-riーtH i ii iiiiii 「T-ri-rコ-T Li-bi. i !! 「ナーF -「i-Fュ…

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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)=…

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Q: 6. Show that F = [y? cos x + z3, 2y sin x – 4, 3xz2 + 2] is a conservative force field. Find the…

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Q: 2 Find the orthogonal trajectories of r=asin? 0 where a be the arbitrary constant.

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Q: 3. Show that the vector field F = -C with C> 0, is conservative and find its potential.

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Q: A particle at (5, 0) traverses the upper semicircle x² + y² = 25 and then closes the loop along the…

A: Formula: The work done by the force F→ is given by, ∮CF· dr, where C is the path along the region.…

Q: 6. Show that the system with vector field -x + sin(y) F(x, y) : -y+ cos(x), admits no periodic…

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Q: The integral of the vector field F(x, y) = (cos |x|, sin y|) A = (-2,0) and final point B (0, 2),…

A: Correct answer is (B) sin(2) - cos(2) + 1 Explanation:

Q: Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?

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Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F = 8 sin 8x cos 5y…

A: We have to find work done.

Q: 2: Compute the work done by the force field F = (y, -x) to move an object from point A = (1,0) to B…

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Q: Express the vector field D = ( x2 + y2 )-1 ( xax + yay ) in cylindrical components and cylindrical…

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