The surface S consists of the four sides of the cube [0, 1] × [0, 1] × [0, 1] plus its top but not the bottom (so the face where z = O is not part of S). If F(x, y, z) = ze*“ i + 3yj + (2 – yz") k then: F. dS (Suggestion: Use the Divergence Theorem, but notice that S is not closed, so you will have to "close it up.")

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

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Q: find the divergence of F at the given point. F(x, y, z) = ei + ej+ek at (3,2,0) div F = 0 div…

A: Given F(x, y, z) = e-xyi + exzj + eyzk

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

A: Given vector field is  Divergence theorem

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: 5. Use the Divergence Theorem to evaluate [[F•d$ where F = yx² i +(xy² - 3=*)j+(x² + y² )k and S is…

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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: 7. Use the Divergence Theorem step by step including sketch of the solid shape to find the flux f SF…

A: sketch of the solid shape is as follows

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: Verify Divergence theorem for the function F = ēpp over the semi-cylindrical volume V = S x² + y² <…

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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: Let F=2xi + 3yj + z2k, and consider the three - dimensional volume inside the cube with faces…

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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: 3. Use the Divergence Theorem to evaluate F.dS where F = -zyi+(z – 1) j +k and S is the surface of…

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Q: Q1. Verify Divergence theorem for the function F = ë,p over the semi-cylindrical volume x? + y? < a…

A: Given the function  F→=e→ρρover the semi cylindrical volume V=x2+y2≤a0≤z≤h, x≥0

Q: 1. Use the Divergence Theorem to evaluate /| F.dš where F.dSv F = yx? i+ (xy? - 324) j+ (x³ + y?) k…

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Q: 2. Using left side of the divergence theorem, find the total charge enclosed in the rectangular…

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Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + 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: Evaluate both sides of divergence theorem for A = pa, + pcos()a,+ za, through the closed surface…

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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 SI div F av F. dS S E for F(r,y,2) = z i+ yj+xk and where E is the…

A: Given that Fx,y,z=z i+ y j +x k and E is the solid ball x2+y2+z2≤16. First find the divergence of F.…

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: Q5. Analyze and Verify Gauss divergence theorem for F 2 xz i+ yzj+ z? k over the upper half of the…

A: Here, F=2xzi+yzj+z2k Given upper half of the sphere x2+y2+z2=a2. Let ∅=x2+y2+z2-a2=0…

Q: State what the Divergence Theorem says, using your own words. You may assume that E is a solid in R³…

A: We can state the Divergence theorem .

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: 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: Use the Divergence theorem to evaluate F. · dS where F (x, y, z) = (4x – z²) i+ (x+3z)j+(6 – z) k…

A: Using divergence theorem:  ∫∫SF.ds=∫∫∫V∇F.dv

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: 5. Using Divergence Theorem, calculate the integral ry²dx + yz²dy + zz²dz where S is the upper…

A: Divergence theorem:

Q: 2. Use the Divergence Theorem to calculate the flux of F = (y– x)i+(z– y)j+(y– x)k across the…

A: Explanation of the answer is as follows

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

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Q: 4. Use the Divergence Theorem to evaluate F.dš where F = (4z – 2²) i + (z +3:) j+ (6 – 2) kand S is…

A: Solution is given below..

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

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Q: Verify the Divergence Theorem: ls F- dS where F= (3z + z",y – sin zz, 2z+ ye) and Sis surface of box…

A: We need to find integral using divergence theorem.

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: Q9. Find the value of the right side of Gauss divergence theorem for F = x²ī+ zī+ yz k over the cube…

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

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Q: evaluate both sides of divergence theorem for A= ra,+rcos(8)a , +r²a, through the closed surface…

A: Given problem is :

Q: Verify Divergence theorem for the function F = e,p over the semi-cylindrical volume { x* +y° sa…

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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: 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 / (7xi – zk) · ndA over the sphere S : x² + y² + z² = | S a) by divergence theorem, (b)…

A: a) By divergence theorem, ∬SA. ndA=∫∫∫V∇.A dV Now,  ∇.A=∂7x∂x+∂0∂y+∂-z∂z=7-1=6 By changing to…

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

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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…

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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Q: Let F(x, y, 2) = 32?ai+ (y³ + tan(z))j+ (3x²z- 4y?)k. Use the Divergence Theorem to evaluate fs F dS…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.