b) Use the divergence theorem to compute ff, F ñ ds, where S is bounded by x+ y + 2z = 2 located in the first octant and F = (2x² - y², 4xz – 2y, xy). %3D

Q: Verify divergence theorem for f=x2i+zi+yzk taken over the cube bounded by x=0,x=1,y=0,y=1,z=0 and…

A: Use the divergence theorem to solve this problem.

Q: 1. Use the Divergence Theorem to evaluate F.dS where F (3z – za) i+(- 1) j+ (4y +) k and S is the…

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Q: Use the divergence theorem to evaluate || F•ndS where F(x,y,z)=xi+ yj+zk . n is the outer unit…

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Q: 3.4.13 Verify the divergence theorem [[ F. JS = [] F.dS div F dV S for F = 4xi-2y²j+z²k over the…

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Q: Let F(x, y, z) = 6x?i – cos(xy)(i + 5). Calulate the divergence: div F(x, y, z) =

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Q: Use Green's Theorem to evaluate | F nds, where F = (Va+ 5y, 4x + 5y) %3D C is the boundary of the…

A: We have to evaluate the integral ∫CF→·n→ds, where F→=x+5y,4x+5y. Where C is the boundary of the…

Q: Use Green's Theorem to evaluate: So F.ñ ds C where F = (Vx + 6y, 2x + 6y) and C is the boundary of…

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Q: If F= 2y I- 3J +x²k and s the surface parabolic cylinder y= 8x in bounded by the planes OF the 2.…

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Q: Use Green's Theorem to evaluate: F.n ds where F = (Vx + 3y, 2x + 3y) and C is the 2x – x2 boundary…

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Q: Find the divergence at Iol g0o o) for Hure Vcetor Ficuld F (Xoyaz) =e*sínyi-c" ă cos yjt z°k

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Q: Use Green's Theorem to evaluate F. nds, where F = (Va + 4y, 2æ + 4y) C is the boundary of the region…

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Q: Evaluate both side of divergence theorem for cube define by -0.1< x. y.z<0.1 if D = 6xe2Y (āx + xay)

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Q: 2. Use the Divergence Theorem to evaluate F.dS where F = 4x i + (1 – 6y) j +k and S is the surface…

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Q: 2. For F(x, y,z)=[5ysec (xy)+6z°eli+ )- 3 | 5x sec (xy) y 3 k, find the curl and the divergence of…

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Q: Q1. Verify Divergence theorem for the function F = ēpp over the semi-cylindrical volume x2 + y? < a…

A: Given:- →F=→eρρ V=x2 +y2≤a0≤z≤h,x≥0

Q: Let E be the region bounded by the hemisphere x² + y? + (z – 2)² = 4, 2 < z < 4, and the plane %3D z…

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Q: Use Green's Theorem to evaluate F nds, where F = (Va + 6y, 3x + 6y) C is the boundary of the region…

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Q: Use the Divergence Theorem to evaluate ff F-n do where S F(x, y, z)=(x² +cos yz, y-e², z² + x²) and…

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Q: Use Green's Theorem to evaluate F. nds, where F = (Va + 6y, 3æ + 6y) C is the boundary of the region…

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Q: Verify the divergence theorem for F = 3 i + xy j + x k taken over the region bounded by z = 4 −…

A: According to the given information, it is required to verify the divergence theorem for,

Q: Verify the Divergonce Theorem for F=(2x-x)+x*y} -aż? taken over the bounded by x -o, X=1, y=0,…

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Q: |s, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xỉ + yj…

A: Answer  Flux = 2π

Q: Use Gauss Divergence theorem to calculate (5zi+ 4yj- 2z k).n dA over the sphere S: 2 + y? + 22 = 9.

A: This is a problem related to vector calculus. Based on the general formula of gauss divergence…

Q: Use Green's Theorem to evaluate F. ňds, where F = (Va+ 6y, 3z + 6y) C is the boundary of the region…

A: Solving this by green theoram

Q: (15) Use the divergence theorem to evaluate SSF. ds, where S 3 F(x, y, z) = and 5 is the surface of…

A: To evaluate the given integral using divergence theorem.

Q: Use the divergence theorem to evaluate ∬S F⋅N dS for F=xyzj, where S is the cylinder x^2+y^2=9, 0≤ z…

A: Use the divergence theorem to evaluate:∫∫SF→·n→dS for F→=xyzj^,where S is the cylinderx2+y2=9,0≤z≤5…

Q: Verify Gauss Divergence Theorem for F = xy²î + yx²j+ek for the solid region D bounded by z = √x² +…

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Q: Q3. Verify the divergence theorem for F = 3 i+ xy j+x k taken over the region bounded by z = 4 – y?,…

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Q: 5) S, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xỉ +…

A: Given: F(x, y, z) = 2xi + y + zk along, almost every where with z = x² + y² paraboid and z = 2x…

Q: Evaluate both sides of divergence theorem for A = pa, + pcos()a,+ za, through the closed surface…

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Q: If D = 15p sin 2øa, + 10p² cos 2pa, C/m², evaluate both sides of the divergence theorem for the…

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Q: Given the field D = 6sin 0.50 a, + 1.5p cos 0.50 a, C/m². Show the divergence theorem is true for…

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Q: Use Green's Theorem to evaluate nds, where F = (Va+ 3y, 2a + 3y) C is the boundary of the region…

A: Given Vector field is  F=x+3y, 2x+3y Comparing with F=P,Q, we get  P = x+3y            and…

Q: -> Verify Divergence Theorem for the function F x + y? = 9, z = 0 and z 2. = yi + xj + z? k over the…

A: Given :-  Verify Divergence Theorem for the function  F→ = y i^ + x j^ + z2 k^ over the region…

Q: Given i = x²& + xy ŷ + yz 2 check the fundamental theorem of divergence over a cube whose each side…

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Q: Use Green's Theorem to evaluate F ňds, where F = (Va + 3y, 2x + 3y) C is the boundary of the region…

A: Greens theorem if u(x,y) and v(x,y) are continuous functions of x and y ;∮  u dx + v dy = ∬(∂v∂x -…

Q: Verify the divergence theorem for F = 3 i+ xy j + x k taken over the region bounded by z = 4 − y2, x…

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Q: Use Green's Theorem to evaluate F nds, where F = (Va+ 3y, 2æ + 3y) C is the boundary of the region…

A: Given information is: Vector field :

Q: Evaluate the integral F•ndA directly or, if possible, by the divergence theorem. F = [3y, –3x, 0],…

A: From Gauss divergence theorem, we have∬SF→.n^ds=∭DdivF→dV=∭D∇.F→dV

Q: Find the divergence of F(x, y, 2) = x²zi + xy²j + (v² + 2)k. Select the correct answer below: O 2xz…

A: Use the method of divergence to solve this problem.

Q: b) Use the divergence theorem to compute f. F ·ñ dS, where S is bounded by x + y + 2z = 2 located in…

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Q: b) Use the divergence theorem to compute ff, F · i ds, where S is bounded by x +y + 2z = 2 located…

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Q: Evaluate both sides of divergence theorem for A = pa, + pcos(ø)a, + za, through the closed surface…

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Q: Use the Divergence Theorem to evaluate |F.n do where F(x,y,z)=(x² +cos yz, y – e" ,z² +x*) and S is…

A: According to question given :F(x,y,z)=x2+cos yz, y-ez, z2+x2S is the boundary of the solidBounded by…

Q: Use the Divergence Theorem to evaluate J] F. ds where F (x, y, =) = , and S is the unit S ball x +…

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Q: Compute s F=

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Q: Use the Divergence Theorem to evaluate F. dS where S is the sphere r² + y² + z² = 9 and F = (3r, 2y,…

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Q: 2. Evaluate , dV, where o= 45 x²y and V is the closed region bounded by the planes 4x + 2y +:=8, x=…

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Q: Use the transformations u = xy and v=xy* to evaluate ff xyd4 where R is the √√3 1 X region bounded…

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Q: use the Divergence Theorem to find the outwardflux of F across the boundary of the region D. F = (x…

A: To Determine: use the Divergence Theorem to find the outward flux of F across the boundary of the…