Determine minimal conditions on the real constant u so that (0, 0) is a center for the linear system x' = -ux + y y' = -x + µy. lµl ? v

Q: A fluid has density 1200 kg/m3 and flows with velocity ī measured in meters, and the components of ū…

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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: A fluid has density 1200 kg/m and flows with velocity = i + yj + zk, where x, y, and z are measured…

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Q: 1. The solid bounded by y = 1, y = x², z = 0 and z = y AS A Z-SIMPLE SOLID.

A: Givne that  Solid region y=1,y=x^2,z=0 and z=y  To find the triple integral

Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 0, z 2…

A: flux is determined as shown below

Q: Find the flux F(x, y, z) = (xy²,x²y, ln(x + y)) directed outwards through the surface of the solid…

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Q: Find the flow of F=xzi-yk through the upper part of plane z-1 in the x +y² +z = 4sphere. %3D

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: 17. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: Let G be the wedge in the first octant that is cut from the cylindrical solid y2 + z2 ≤ 4 by the…

A: In the first octant, all the coordinates are positive, i.e. x≥0, y≥0, z≥0. So we will take all the…

Q: A fluid has density 1000 kg/m³ and flows with velocity = ci +yj + zk, where x, y, and z are measured…

A: We have to find the rate flow outward through the part of paraboloid . We can to use the methods of…

Q: 3. Find the displacement u(r, t) in a vibrating circular elastic membrane of radius 1 that satisfies…

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Q: If F= represents the flow of a liquid through a parabolic cylinder S: y=x, 0sxs2, 0szsl. That is…

A: If F→=y2,-x2,z2 represents the flow of a liquid through a parabolic cylinder S:y=x2,0≤x≤2,0≤z≤1.…

Q: A fluid has density 1000 kg/m3 and flows with velocity ū = xi + yj + zk, where x, y, and z are…

A: A fluid density 1000 kg/m3 andflows with velocity v→=xi→+yj→+zk→where x,y and z are measured…

Q: Compute the flux of F = 3(x + z)i +j+3zk through the surface S given by y = x2 + z2, with 0 0, z >…

A: From given data we see that the surface is oriented towards xz plane,  Hence,  d→s=dxdzj→

Q: 1. Verify that (t) = et, y(t) = e' satisfies the system %3D dx 3y3 dt dy y, dt %3D

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Q: Show the triangular region bounded by the lines x = 0, y = 0 and x + y = 1 is invariant for the…

A: Given: It is given that, the triangular region is x=0, y=0 and x+y=1. To prove: We have to prove…

Q: A solid cube, 2 units on a side, is bounded by the planes x = +-1, z = +-1, y = 3, and y = 5. Find…

A: Given:

Q: 2). Find the flux of F(x, y, z) = (0, yz, z) outward through the surface S cut from the cylinder y +…

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Q: The solid bounded by the paraboloids 2= - 8+z²+ y² and z -3-32²-3y² has volume:

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Q: Calculate the line integral F(x, y, z)=2xy^2 i+(2yx^2 +2y)j     on a path from (0, 0, 0) to(3, 1, 1)

A: We need to compute the line integral: F(x,y,z)=2xy2i+(2yx2+2y)j on a path from the point: 0, 0, 0 to…

Q: Determine the centroid, C(X,9.2). of the solid formed in the first octant bounded by z+y- 16 = 0 and…

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Q: Find a solution to the Dirichlet boundary value problem for a disk. zu 1 du 1 Pu = 0, + -- ar? Osr<…

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Q: Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of…

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = xy + yz + xz…

A: Function: f(x,y,z)=xy+yz+zx, at(0,0,0) We need to find fx,fy,fz. at the point (0,0,0)

Q: 4. (Section 17.8) Use the Divergence Theorem to calculate [[F F-dS, where F = y + ryj – zk and S is…

A: To use the divergence theorem to calculate ∫∫SF⋅dS.

Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 <y<9, x…

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Q: Determine the centroid, C(x̅, y̅, z̅), of the solid formed in the first octant bounded by y = 4−x2…

A: Given curves are

Q: Find the counterclockwise circulation and the outward flux of thefield F = (-sin y)i + (x cos y)j…

A: Use tangential form of Green's Theorem to find the counterclockwise circulation. Counterclockwise…

Q: Consider the Hamiltonian flow on R² associated to H(x, y) = }y² + x(x – 1)(x + 1). Show t (11 2 0)…

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Q: Use the Divergence Theorem to evaluate       SF · N dS and find the outward flux of F through the…

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Q: 2. Calculate the circulation of the flow v=-8xy i+ 4 yj around the triangle with vertices (0, 0),…

A: Given that: v=-8xyi+4y2j The triangle is with the vertices (0,0), (3,0), (3,2) To calculate the…

Q: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…

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Q: 5/ MATH

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Q: 5. Find the flux of F (x,y,z) = y cos(z)i-yx sin(x) j+ xy³k through the outward oriented cube of…

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Q: Determine the centroid, C(x,5,z), of the solid formed in the first octant bounded by y = 4 – x² and…

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Q: 2) Find the outward flux of F across the region D where F(x, y, z) = (In(x² + y²), –tan'(), zVx² +…

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Q: Compute the flux of F(r, y, z) = [1,–2, z] through the surface S, which is part of the graph z =…

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Q: Consider the gradient flow associated to V (x, y, z) (x, y, z) = (0,0, 0) is an unstable…

A: To check whether an equilibrium point is unstable we have to find wheather that point corresponds to…

Q: Verify Stokes' Theorum for F(x,y,z) = (y,-x,yz) if S is the paraboloid z = x2 + y2 with x2 + y2 = 1,…

A: Given  Fx,y,z=y,-x,yz Then, F→=yi^-xj^+yzk^

Q: Find the flux of F(x, y, 2) = (r, y, 2) across the surface o which is the surface of the solid…

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Q: 5. Compute the flux of F(r, y.2) =zi- 2yj+ 2ak across the surface of the cylinder bounded by a+y =9…

A: Solve the problem as shown below.

Q: 16. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: c, y, z) = x²zi + xz'j+ y ln(x + 1) k, s the surface of the solid bounded by the 2z = 4, y = 3, x =…

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Q: 4. Determine which of the following sets of velocity components u and v satisfy the equation of…

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Q: (7) Determine the upward flux of V x F through the part of the elliptical cone C = {(x, y, z)2 =…

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Q: dy _ у-х dx 1+x y(0) =1 at the point x=0.1

A: Given differential equation is dydx=y-x1+x,y0=1.

Q: (a) Integrate g(x,y,z) = lnx'+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 2. The solid in the first octant bounded by the planes x = 0, y = 0, z = 1, z = 2 – y, and the…

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