F(x, y, z) = y ₁ + 2 z j + X²k 2 2 z=4-x² - y², zzo. and let S be the paraboloid 1) Calculate curl F 2) Compute the surface integral SS curl F.IS, where the parameterization of S is the canonical or stender: X= X y= y Z=4-x² - y²

Q: Verify Stokes' Theorem for S given by S = {(x,y, z) : z = x(1- x),0 <x < 1,0 < ys 1} and the vector…

A:

Q: 4. Curl of f (x, y, 2) = 2æyi + (x² + z²)j + 2zyk is a) xy? i- 2xyzk & irrotational b) 0 &…

A: find curl ,

Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

A:

Q: (iv) and (0, -1) to (1, 1). Find the circulation of F round the curve C, where F=e* siny i + e*…

A: Circulation of a vector field about a contour is the line integral of the vector field when it is…

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

A:

Q: Let S be the surface defined by the vector function R(u, v) = (v + 4, 4u - v, uv²). Set up an…

A:

Q: Verify Stokes' Theorem for S given by S = {(x,y, z) : z = x(1- x),0 <x < 1,0 < ys 1} and the vector…

A:

Q: e Il Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = x²z² + y²z²j + xyzk, S is the part of…

A:

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: A normal vector to the tangent plane for the surface z = , at the point (1, 1, 1) is: y - Select…

A:

Q: Let vector field F =(x,y,z²) across the surface S which is an upper hemisphere x²+ y² + z² = 4 . 1)…

A: Let vector field F =(x,y,z²) across the surface S which is an upper hemisphere x²+ y² + z² = 4 . 1)…

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

A:

Q: and Verify Green theorem where F = 2xi-Y2j+ŻK s it represents the Surface generated by the Parabolic…

A:

Q: If F(x, y, z) = –2i – 2æj – yk and G(x, y, z) = –2xi – yj – 2zk, find curl(F × G).

A:

Q: Jse Green's Theorem to evaluate the line integral along the positively oriented closed curve C.…

A: The equation of a straight line joining two points x1, y1 and x2, y2 is given by the formula: y-y1 =…

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

A: Parametrization

Q: Apply Stoke's theorem to compute ||curl F-ds where C is the triangular closed path Toining the point…

A:

Q: Verify Stokes' Theorem for S given by S = {(x,y, z) : z = x(1- x),0 <x < 1,0 < ys 1} and the vector…

A:

Q: evaluate ∬s curl F*dS F(x,y,z)=x2sinz i+y2j+xyk S is part of the parabaloid z=1-x2-y2 that lies…

A:

Q: Use Green's theorem for the work done by the force F= (x - y)i + (x + y)j, for the shaded region R…

A:

Q: Verify Stokes' Theorem for S given by S = {(x,y, z) : z = x(1- x),0 <x < 1,0 < ys 1} and the vector…

A:

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…

Q: Let r(u, v)= [2usin(v), 2ucos(v), 2] be a parametrization of a surface S, where 0sus2,0svs27. Then…

A: Given surface is  ,

Q: Use Green's Formula to evaluate the line integral along the positively oriented closed curve C:

A:

Q: 6) Apply Fundamental Theorem of eine Integrals ntegral to evaluate the line where C is the square…

A: Given, ∫chx,ydS=∫c3x2y+xy2-1i^+x3+x2y+4y3j^dS=∫c3x2y+xy2-1dx+x3+x2y+4y3dy