Use Stokes' Theorem to evaluate 16. curl F. ds. F(x, y, z) = 6y cos(z) i + ex sin(z)j + xey k, S is the hemisphere x² + y2 + z² = 49, z ≥ 0, oriented upward.

Q: Use Stokes' Theorem to evaluate curl F- dS where F(r, y, 2) = 4ryzi – ryj + x?yzk and S consists of…

A:

Q: * +(x) = 3x6-4 (x-k)² +17, the value of the parameter k for f(x) to be a function pair IS?

A: For f(x) to be a function pair  it needs to be one-to-one, which means that each input value must…

Q: Find the equation for the rectifying plane at the point that corresponds to that value of t. r(t) =…

A:

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = 4y cos(z) i + e\ sin(z) j + xeY k, S is the…

A: Given that Fx,y,z=4ycoszi+exsinzj+xeyk and S is the hemisphere x2+y2+z2=9,z≥0. The expression for…

Q: F(x, y, 2) = 2y cos(2) I+ e sin(2) j + xe k, S is the hemisphere x + y? + 22 = 9, z 2 0, oriented…

A: Surface integration

Q: 4. Use Stokes' Theorem to evaluate curl F.dS where F = (x-y, yz, xz) and S is that part of the…

A: Step 1We have, ∫∫curlF.dsStep :2 CurlF=∣∣∣∣∣∣∣​i∂x∂​f1​​j∂y∂​f2​​k∂z∂​f3​​∣∣∣∣∣∣∣​Step 3Here…

Q: The curl of f(x,y,z)=xyzj is =.

A:

Q: Use Stokes's Theorem to evaluate e curlF. ds. (1) F(x, y, z) = x²y³zi+sin(ryz)j + xyz k, S is the…

A: “Since you have posted multiple questions, we will provide the solution   only to the first question…

Q: F(x, y, z) = tan-'(x?yz²)i + x²yj + x²z?k, S is the cone x = V y2 0 <x < 4, oriented in the…

A: Define curve C with boundary curve: r→=4i^+4costj^+4sintt^

Q: @ Sahe the wibrating hring problem. uco,E) = u(#,t)=0, u(x,o) = $in (2x) + sin (3x). Uelx,0) =…

A: In the given question we have to solve the given wave equation. Concept: The given wave equation is…

Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A:

Q: Ic F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 5zj + 7yk,…

A:

Q: Use Stokes' Theorem to evaluate |/ curl F. dS. F(x, y, z) = tan-(x²yz²)i + x²yj + x²z?k, S is the…

A: Stokes' Theorem:                                 ∮C F .dr =∬S curl F. dS Where C is the boundary of…

Q: Consider the contour represented in the following figure. The points marked on the figure are А(3,…

A:

Q: Let F = . Use Stokes' Theorem to evaluate curlF rlFds, where S S is the hemisphere x² + y² + z² = 4,…

A: I have explained everything with in the solution, please go through that.

Q: Use Stokes' Theorem to evaluate Use Stokes' Theorem to evaluate ∫C F · dr where C is oriented…

A:

Q: H.W: Select the divergence of F(x, y) i+ (2x – 3y)j. %3D 1 (b) -* +2, y2 1 (c) (a) 3, (d) -2. - - -

A: Multiple:   Divergence of a vector field find by taking the scalar product of the vector operator  ∇…