What is the largest possible magnitude of Curl(F) where F(x, y, z) = (4, a/9 – y?, 6z)? у, х

Q: Evaluate the line integral fc (2 + x*y)s, where C is the half circle x + y? = 1 in the upper half…

A:

Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = xyzi + sin(xyz)) + xyzk, S is the part of…

A:

Q: Find the area and centroid bounded by the curve 5y? = 16x and the curve y2 = 8x – 24.

A: Since you have asked multiple question, we will solve the one question for you. If you want any…

Q: What is the normal vector, n for S is a surface of x +y² +z² = 36 in the first octant? %3D

A:

Q: 6. Compute the area of the surface for 0 <u 1, 0 < v < using the first fundamental form..

A: Given xu,v=u2-cosv,u+sint,cosv

Q: Find the circulation of F(x, y, z) = (-y sin 2, x sin z, xy cosz +12) around the circle cut from the…

A: Given that,F(x, y, z)=(-ysinz, xsinz, xycosz+12) around the circle cut from the sphere x2+y2+z2=5 by…

Q: Compute the moments of the semicircle x2 + y2 = R2, y ≥ 0 as line integrals. Verify that the…

A: Given semicircle x2+y2=R2,  y≥0 The figure of this semicircle is shown below. In the above figure,…

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A:

Q: Use the Divergent Theorem to find the outward flux ofF = yi+3yj+ 322k across to the boundary of the…

A:

Q: (2) Use Stoke's theorem to evaluate the integral curl where S is the surface given by 2= et-- - 1, 2…

A:

Q: Use Green's Theorem to evaluate the line integral: f. In(1 + y) dr – #, dy where C is triangle with…

A:

Q: Use Stokes' Theorem to find the line integral of F = 3yi + 2zj + 5xk around the triangle obtained by…

A: Given function is F→=3yi^+2zj^+5xk^. We have to evaluate the line integral of F→ around the triangle…

Q: By using two methods, find the work done by the force field F(x, y) = ysin xỉ + xe³ ĵ to move a…

A: Given: To compute:  ∫C F.dr=?F→(x,y ) = y sin x i^…

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

A: The objective here is to evaluate: ∬ScurlF⋅dSWhere, Fx,y,z=tan−1x2yz2i+x2yj+x2z2k; and S is the cone…

Q: Use Stokes' Theorem to evaluate the integral: [cur S curl F. dS F(x,y,z)=ze' i+xcos (y) j+xzsin (y)…

A:

Q: 2/ MATH

A:

Q: Use Stokes' Theorem to evaluate SSs curlF · dS, where F(x, y, z) = 7xyi + 3yzj+4z²k and S is the…

A: Consider the provided question, Use Stokes' Theorem to evaluate ∫∫Scurl F·dS,where F(x, y, z)…

Q: 2)Use Stokes' Theorem to evaluate [F.dr where E2xyi, y² j‡ 2xzk and Sis the first octant с surface…

A:

Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

A: Solution:

Q: 339. Use Stokes' theorem to evaluate curl F · dS, where F(x, y, z) = e®Ycos zi + æ²zj+ xyk, and S is…

A: please see the next step for solution

Q: Evaluate Curlv.ñ , where v = 2xyi +(x² – 2y)j + xzk and ñ is a unit vector normal to the surface…

A:

Q: Let F = . Use Stokes' Theorem to evaluate / curlF · d5, where S is the hemisphere x² + y² + z² =…

A:

Q: Set up the surface integral for upward Flux of the upper hemisphere of radius = 5 (z20) such…

A:

Q: Find the centroid of the surface formed by the revolution of cardioid r = a(1 + cose) about the…

A: Given equation of cardioid, r=a1+cosθ Let the centroid be x,y.

Q: 4) Use Stokes theorem to evaluate SF.dr, where с F(x, y, z) = <.xy, yz, *x), where C is the triangle…

A:

Q: Evaluate the surface integal [[Curl F.ñ dS for the Sur face and F=xt-y²+ (x+4+z)Ñ and C is the bo…

A:

Q: Use Stokes' Theorem to evaluate curl F. dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part of…

A: Stokes theorem: ∫∫ScurlF.dS=∫CF.dr

Q: Evaluate the flux integral ff. curl (z cos x i+yj+x sin y k) ds where S is the part of the outward…

A:

Q: 9) Use Stokes' Theorem to evaluate || curl (F)· dS where F(x, y, z) = (x sin z)i+(x)j+(xy)k and S is…

A:

Q: Use Stokes' Theorem to evaluate curl F · dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part…

A:

Q: Determine the element of surface area dS in the special case of the paraboloid of revolution z = x2…

A:

Q: Calculate the points of intersection of the curves x² = 4y and bn=) = y 29vaus at newed biloa gris 1…

A: Centroid: The centroid or centre of mass of a region bounded by the curves is the point where the…

Q: Evaluate the circulation of G = ryi + zj + 2yk around a square of side 7. centered at the origin,…

A: Given  G=xyi+zj+2yk around a square of side 7

Q: Compute the surface integral of the normal component of F(x,y, z) = xi over the triangle with…

A: According to the given information, it is required to calculate the surface integral.

Q: Calculate the curl and divergence of F(x, y, z) = x² sin yz i+ z cosxz j+ ye5y k at point (0, 1, 2).

A:

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A:

Q: Use Stokes theorem to evaluate ff.curl F.nds. where F = (xyz, x, e* cos z), while S is surface x² +…

A: Solution :

Q: '. Use Stokes' Theorem to compute || CurlF •dS for the hemisphere x + y +z² =9, z20, intersected…

A:

Q: 2. When F = (y z, xz, x² y?) and S is the part of the paraboloid z = x? + y? that lies in the…

A: First, we have to parametrize the surface to apply the Stokes theorem.  Part of the paraboloid is…

Q: Evaluate the circulation of Gayi + zj+5yk around a square of side 9, centered at the origin, lying…

A: Solution :

Q: Does the integral of f(x, y) = 1/(1 – a² – y²) exist over the disk a? + y² < 1? Explain. -

A:

Q: Use Green's Theorem to evaluate the integral |x?ydx + xydy where Cis the rectangle with vertices (0,…

A: To evaluate: The integral ∫Cx2ydx+xydy. Given information: The vertices of the rectangle is 0,0,…

Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

A:

Q: What value of z in the interval 0< z< 2 corresponds to the greatest magnitude of Curl(F) where F(x,…

A: Given: F→(x,y,z)=tan(x),y4,2xcos(z-1)

Q: 2)Use Stokes' Theorem to evaluate | F.dr where F =2xyi- yj+2xzk and S is the first octant surface of…

A: The given problem is to evaluate the line integral in the surface of first octant with upward…

Q: Find the divergence and curl of F = (e¬* sin y , e¯Y sin z , e-² sin x). %3D

A:

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F =xi+ 5xj +zk…

A:

Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

Q: Use Stokes' Theorem to calculate fe F-dĩ, where F = zyi+3=j+5zk, and C is the closed path around a…

A: Here given that F→=xy i^+3z j^+5x k^ and curve C in xz-plane. To find: ∫C F→·dr→ by Stokes' theorem.

Q: 'Use Stokes' Theorem to compute | 1 F. dr where C is the curve where the cylinder a? + y? = 1…

A: