1. Use the Divergence Theorem to evaluate F.dS where F (3z – za) i+(- 1) j+ (4y +) k and S is the surface of the box with 0< <1, -3

Q: Q2. If F = (x² - y² + 2xz)ī− (2xz − xy + yz)j + (z² + x²), find the divergence of curl F and curl of…

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Q: 4. Given F(x, y, z) = (xy²z²)i + (x²yz²)j + (x²y²z)k Find: a. Curl b. Divergence

A: Use the formula of both Curl and Divergence to determine their values. In partial differentiation,…

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: Suppose that f, g € H(D(z,r)), 1 < m < n, f has a zero of order n at z and g has a zero of order m…

A: Given that fz1 has zeros of order n at z ⇒fz1=z1−znϕz1 where ϕz1≠0 And gz1 has zeros of order m at z…

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: Use the Divergent Theorem to find all values of b> −1 such that ∫∫SFdS = (45b/2) + (51/2), where F…

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Q: 5. Let F(x,y,z) = (3xy²)i + (xe²)j+ (z³)k. S is the closed surface bounded by the cylinder y? + z? =…

A: 9π/2

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: Use Green's Theorem to evaluate C |F.nds, where F = (Va+ 3y, 20 + 3y) C is the boundary of the…

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Q: Verify Gauss Divergence Theorem for F = (x3- yz)i+ (y² - xz)j+ (z3 – xy)k %3D taken over a…

A: GivenF→=x3-yzi^+y2-xzj^+z3-xyk^taken over a rectangular  parallelepiped bounded by 0≤x≤a,0≤y≤b and…

Q: Let z = f(x, y) = x² – y² + xy + 2. Consider the triangular region in the xy-plane with corners at…

A: The given function is z=fx,y=x2-y2+xy+2

Q: 5 Evaluate F.ds over the surface S defined by x² + y² + z² = 4 for z ≥ 0 and bounded by x = 0, y =…

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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: Suppose that (z) is entire and that the harmonic function u(x, y) = Re[fz)] has an upper bound uo;…

A: As requested following is the answer for question 12.

Q: 7. Use the Divergence Theorem to evaluate ff(F n) dS, where S is the top half of the sphere r+y + z…

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Q: Verify the divergence theorem for F=3i + xy j + x k  taken over the region bounded by z = 4 - y^2 ,…

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

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

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Q: Verify the divergence theorem for F= 3i+xyj+xk taken over the region bounded by z = 4-y^2 , x=0 and…

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Q: 7. Use the Divergence Theorem to evaluate ff(F n) dS, where S is the top half of the sphere r2 +y +…

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Q: Find the divergence of F(x, y, z)= x î+y³ ₂² 7 +xz³ k. O1+3y²z²+3xz O1+3y²z²+3xz² 01+3y²₂² O 1

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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: -> 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: Calculate the divergence of cach of the following functions (a) r²î + y²§ + 2²k. (b) yzî + xzj+ xyk.…

A: As per the instruction, we will answer only the first 3 subparts. For (a), For a given vector fx, y,…

Q: Find the value of the right side of Gauss divergence theorem for F = x²ī+ zī+ yz k over the cube…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 1, Evaluate & FdV where V S is bounded by the planes x=0, x=2₁ y = 0, y = ²,2 = 1, and F=64²³yo, 2…

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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 − y2, x…

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Q: Given the field D = 6p sin 124 ap +1.5p cos 12 a, C/m2, evaluate both sides of the divergence…

A: field D=6ρsin12ϕ ap + 1.5ρcos12ϕ aϕ C/m2 here ∇ = aρ ddρ + aϕddϕ+azddz Divergence = ∇·D ∇·D=…

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

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Q: Suppose we have a surface f (x,y)=x²y+cos (4x) · Which of the following is the gradient of f(x,y) at…

A: First I have found the partial derivatives of f(x,y)  with respect to 'x' and 'y' at point P(π/2,…

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: Find the divergence of F = (1 + xy)i - y°z?j - xz°k | Select one: 2 2 O a. x-3y z-3xz? а. х-Зу z…

A: We have to find the divergence of F=(1+xy)i^-y3z2j^-xz3k^ .

Q: 4. Verify Divergence Theorem for F =x?i + zj + yzk, taken over the cube bounded by x= 0, x = 1, y =…

A: Gauss divergence Theorem.  Let v be volume bounded a closed surface S and F be a vector…

Q: evaluate.both sides of divergence theorem for A= ra,+rcos(e)a, +ra, through the closed surface…

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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: Evaluate both sides of divergence theorem for A= pa, + pcos(6)a+za, through the closed surface 0<p<…

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

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Q: 53. Verify the divergence theorem for A = 2x?y i – y² j + 4xz2 k taken over the region in the first…

A: Given : A=2x2y i- y2j + 4xz2 kbounded by y2+z2=9 and x=2

Q: Find the divergence of F. F(x, y, z) = 8xi + 8y²j + 8z²k

A: Given,           Fx,y,z=8x2i+8y2j+8z2k

Q: 3) Find the divergence and curl of f3xi+ 5x} j + 2y²k, at the point (1,2,3)

A: Solution is done in step 2

Q: Use the divergence theorem to evaluate Is F·N dS, where F(x, y, z) = yʻzi + y°j + xzk and S is the…

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

A: Given A=ρaρ+ρcosϕaϕ+zaz and the closed surface is 0≤ρ≤1, 0≤ϕ≤π, 0≤z≤2. We have to evaluate the both…

Q: Let F(x, y, z) = 4z²ei+ (y³ + tan(z))j+ (4x²z – 3y²)k. Use the Divergence Theorem to evaluate f, F .…

A: Given,       F(x, y, z)=4z2xi+43y3+tan(z)j+(4x2z-3y2)k use the divergence theorem to evaluate…

Q: Evaluate both sides of divergence theorem for A= pa, + pcos(0)a , + zaz through the closed surface…

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Q: 8. Let F = 2 (in 2D). Show that F is divergence-free on its domain, that is, V.F= 0 at all points…

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