Use Stokes Theorem to evaluate •[F F-dr where F(z, y, z)=zi+si+z²+ y²)k and C is the boundary of the part of the paraboloid where 2-16-2²-² which lies above the xy-plane and C is oriented counterclockwise when viewed from above.

Q: y"+y' - 2y = x2

A: Solution :-

Q: /F-nds, where b) Use Gauss theorem to evaluate F(x, y, z) = (2a²y² + In 2) i – xy° j – tanh(2² + y²)…

A:

Q: Determine the flux of F(x, y, z) = across the surface with an upward orientation. Let the surface…

A:

Q: Jo F-dr where F(x, y, z) = xi+yj + 6(x² + y²)k and C is the boundary of the part of the paraboloid…

A:

Q: Use Stokes' Theorem to find the line integral | (17 + 2y°)i + (w + =°)5 +(= + 2r*)k) • dř where C is…

A: Stokes' Theorem: Let S be a oriented smooth surface which is bounded by the curve C (simple closed,…

Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

A:

Q: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

A:

Q: The distance of a point P(x,y,z) from the xy plane is d = |x| how do we show the work to prove this?

A: To show the distance of a point P(x, y, z) from the xy-plane is d = |x|, it can use the distance…

Q: A solid concrete porch consists of 3 steps and a landing. The steps have a tread of 11 inches, a…

A:

Q: Use Stokes' Theorem to find the line integral [((x² + 2y² ((x + 2y²)i + (y + 2²)j + (2 + 2x²)k) · dř…

A: Given that C is boundary of triangle with vertices 1,0,0,0,1,0,0,0,1 So, equation of the plane with…

Q: Use Divergence theorem to find the outward flux of F = (7x², et², cos³ (y² + x)) of the cube in R³…

A: Given that  and the cube  bounded by the planes The Divergence Theorem

Q: 1 − v2), 0 ≤ u ≤ 2π, v ≥ 0.

A: The surface S is a portion of a paraboloid that opens downwards, truncated at its base. To see this,…

Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

A:

Q: Find g, (0,3). ) Find g2 (0, 3). i) Find the equation of the tangent plane to the surface z = f(3…

A: 1st option is correct

Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

A:

Q: Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = xzi+ xyj+2xz k,•. and C is the boundary of…

A:

Q: Q3] (A) Verify Stokes' theorem where Ã= (x-z)i + (x³ +zy)j - 3x y²k and S is the surface of z =…

A:

Q: Find the flux F(x,y,z)=2xi+2yj+zk across the part of the paraboloid z=4-x^2-y^2 above the xy-plane…

A: We have to find the flux F(x,y,z)=2xi+2yj+zk across the point of the paraboloid z=4-x2-y2 above the…

Q: Use Stokes' Theorem to evaluate fF.dr if F(x,y,z) =( z-y)i +(x+z)]- (x +y)K and C is the curve of…

A:

Q: (ii) Use Stokes' Theorem to evaluate SF · dr, where F(x, y, z) = x²zi+xy²j+z²k and C is the curve of…

A: Given function is F(x,y,z)=x2z i^+xy2 j^ +z2k^ . Plane: x+y+z=1 Cylinder: x2+y2=9 The objective is…

Q: (x², y², z(x² + y²)) around any closed curve on the surface of Show that the circulation of F = the…

A: Circulation of vector field F around a close curve C = ∫CF.ds If parametric equation of curve C…

Q: a) Find the curl V×Fif F = (y',2xy,yz)

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Use Stokes's theorem to evaluate F.dr, where F(r, y, z) = ry i + x°yj+yz k, where C is a triangular…

A: Stroke's theorem:  ∫Fdr=∬ (Curl F) n^dS Curl F=ijkxy2x2yyzy2x2y=iz n^=∇s∥s∥=i^+k^2

Q: Complete the sentence below. Iff is a one-to-one function and f(3) = 6, then f(6) = If f is a…

A: One one functions

Q: Let r(u, v)= [2ucos(v), 2usin(v), 2] be a parametrization of a surface S, where 0 sus1,0svs2n. Then…

A: Parametrization

Q: Evaluate F-di where F(x, y, z)=1li +(x+yz)j+(xy- Vz 3x+2y+z=6 in the first octant. C is a positively…

A: Here we have to evaluate ∫CF→·dr→=? Where F→(x,y,z)=i^+(x+yz)j^+(xy-z)k^ and C is the boundary of…