a. Use the Divergence theorem to calculate ff (vn) do for v(x, y, z) = (x+z)i + (y+z)j + (x+z)k on the surface S: y² +2²=1, 0≤x≤4 b. Calculate the total flux of v(x, y, z) = 2xi+xz j+z²k out of the solid bounded by the paraboloid z = 9-x² - y² and the xy-plane.

Q: Let F(x,y,z) = ztan(y2) i + z³In(x² + 4)j+z k. Find the flux of F across the part of the paraboloid…

A: Given that, F(x,y,z)=ztan-1(y2)i+z3ln(x2+4)+zk To find flux of F: Divergence theorem:…

Q: Use the Divergence Theorem to evaluate [/F. F. N ds and find the outward flux of F through the…

A: Given: Fx,y,z=xi+yj+zkS: x2+y2+z2=4 Using the divergence theorem we have to calculate the outward…

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

A:

Q: Suppose F(x, y, z) = (x, y, 52). Let W be the solid bounded by the paraboloid z = x² + y² and the…

A: Given:  F→x, y, z=x, y, 5z Paraboloid z=x2+y2 Plane z=25 To find:  a ∬S F→·dA→ b (i) Flux out of the…

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

A:

Q: Use the Divergence Theorem to evaluate [/F. F.N dS and find the outward flux of F through the…

A:

Q: 16. Use the Divergence Theorem to find the total outward flux of F = xi + 2yj + 3zk across the…

A: We have to use the divergence theorem and find out the outward flux of  F=xi+2yj+3zkAcross the…

Q: Use the Divergence Theorem to evaluate [/F. F. N dS and find the outward flux of ♬ through the…

A:

Q: Use the Divergence Theorem to evaluate [/F. F-N ds and find the outward flux of F through the…

A:

Q: The volume of the solid bounded by the plane 3x+6y-2z=12 and the coordinate planes is O A. 2-2y+4 1…

A: We need to find the volume of the solid bounded by the plane 3x+6y-2z=12. Now,…

Q: Let F(x, y) = (xy² + 7x, x²y-7y). Compute the flux F nds of F across a simple closed curve that is…

A: It is given that the vector field is . Let  then wehave,  and .We have to compute the flux  of the…

Q: Suppose C is a constant vector. Let F(x, y, z) = C find the flux of F through a surface S on plane…

A:

Q: A conical domain with vertex (0, 0, b) and axis along the z-axis has as base a disk of radius a in…

A:

Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

A: The vector field is F=xi^+yj^+zk^. The curves surface is x2+y2=1 bounded below by the plane x+y+z=2…

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

A: The given vector field is F(x,y,z)=x2 i +y2 j +z2 k and S: x=0, x=a, y=0, y=a, z=0, z=a.  To…

Q: Find the flux of G(x, y, z) = (xz)i+ (yz)j+(z²)k outward across the part of the sphere x² + y² +z² =…

A: Here, surface, S={(x,y,z): x2+y2+z2=9, and 1≤z≤2}. For z=1, we get x2+y2=8 and for z=2, we get…

Q: Let f : R" × Rn → R be defined by f(x,y) = ã³ỹ. Verify that f is a bilinear(2-linear) form on Rn.…

A: To verify that f is a bilinear form on Rn, need to check each of the properties:(a) For vectors…

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

A:

Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(x, y, z) = x²i+ %3D Pj+ z°k.

A: Given: x+32+5y-22=16 Fx,y,z=x2+y2+z2

Q: Determine minimal conditions on the real constant u so that (0, 0) is a center for the linear system…

A: Here is the Answer and Explanation

Q: Let F(x, y, z)=zi+yj+z¹k. Compute the flux of F over the surface S, which is the part of the cone z…

A:

Q: In V = R³. Let W₁ be the xy - plane and let W₂ be the z zxis: 2 and Show - W₁ = {(x, y, 0) : x, y ≤…

A: