Use Divergence Theorem to evaluate ,0²z²i + z²x²j+ x²y²k).ds, 1. where S is the upper part of the sphere x + y + z = 9 above xy- plane.

Q: 7.H Jse the divergence theorem to evaluate where S is the sphere x+y? +? = 4 oriented with outward…

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Q: Use Divergence Theorem to evaluate ,0i +rj +ryh) ds, Q#3(a) where S is the upper part of the sphere…

A: As per bartleby instruction when more then one question is given only one has to be answered. Please…

Q: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D

A: In this question, we have to write the triple integral to find the volume of the solid bounded by…

Q: 3, Consider Hhe following twe suctaces 2=2xy Sur 82- 5y-82=-13 a) Show that the surdaces inter sect…

A: Let the bequation of surface is given by F(x,y,z)=0 and if f is differentiable at point…

Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2i -…

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Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: * Use the Divergence theorem to find , F. dS where F(z, y, z) = (zy, y, -zy) and S is closed surface…

A: Using surface integral, answer is 8π

Q: |Use Green's Theorem to evaluate | -x'ydx+xy°dy where C is the boundary of the C circle x + y =16…

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Q: Consider 2-dimensional hyperbolic space with metric ds ds'+dy and y > 0. The length of a line…

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Q: Miscellaneous volumes Use a triple integral to compute thevolume of the following regions.

A: The given equation of cone is and plane is, z=1-x2+y2 x+y+z=1

Q: b) Use Gauss' theorem to evaluate f[ F· ndS where M UTM = (x² – y)i + y°z²j + (xy – y²z³)k and o is…

A: The given problem is to evaluate the given double integral using gauss divergence theorem over the…

Q: Use Divergence Theorem to evaluate .(v²z²i +z²x²j+x²y²k).ds, where S is the upper part of the sphere…

A: Gauss Divergence Theorem : ∫∫SF·ndS=∫∫∫VdivF dV From ∫∫Sy2z2i+z2x2j+x2y2k·dS, F=y2z2i+z2x2j+x2y2k

Q: Use the Divergence Theorem to evaluate the surface integral (2x^2 + 3yz + 4xz) dS where S is the…

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Q: (1) Use the divergence theorem to evaluate F-S. where F (z, y, 2) = zzi – j+4:k and S is the surface…

A: we use divergence theorem for finding the surface integral.

Q: Determine the projection of the following surface on the xz plane. (xz trace) 4x – + = 0

A: Given equation of surface is 4x-y24+z28=0

Q: Use divergence theorem to evaluate F •dš where F(x,y, z) = (2x + yz)ī + 2yzj – z?k and S is the…

A: According to the divergence theorem ∬SF¯·ds¯=∫V∇·F¯dV, where V is the volume bounded by the closed…

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: 4.) Verify the Divergence Theorem where F(x, y, z)=(x',xz,3z) given by x' + y +z² <4. and E is the…

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Q: Suppose f(x, y) satisfies the basic existence and uniqueness theorem in some rectangular region Rof…

A: Consider the given: Let the function f(x,y) satisfies the basic existence and uniqueness theorem in…

Q: Apply the divergence Theorem,with the surface of F = 4xzỉ – y²j + yzk and S being the cube surface…

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Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

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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: Let F(z, y, 2) = 12?ri + (ty + tan(z))j + (1z?z+ 4y?)k. Use the Divergence Theorem to evaluate f, F…

A: We must apply the Divergence theorem on a closed solid, but the surface S is not closed (it is just…

Q: å:RR→R be defined by dcx.y)=|xl+1yl, HxixR (R,d)is Than a metric space.

A: As per our guidelines we supposed to solve the very first question when the multiple questions are…

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

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Q: evaluate $ A. dš over the sphere R = 3 and show whether Divergence theorem holds or not. %3D

A: Calculate surface integral over R=3 or dr=0 ∮A→×ds→=∮R cos2θ,π,0×r2sinθdθdϕ,rdϕdr,rsinθdrdθ…

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: or tho gonal Use the least, me thad to find the squones projetiom of bz Ġ 2 -a anto the salwmin of…

A: Consider the given:         A=011211and  b=12-2T=12-2

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: 5. Compute / | F. aš, where F = (y, -x, 2z) and S is the surface of the sphere of radius 2, centered…

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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: Use divergence theorem to evaluate where F(x, y, z) = 3xi + xyj + 2xzk and s is the surface of the…

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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 Gauss' theorem to evaluate RR F. ndS where F = (x² - y)i + y³z²j + (xy – y²z³)k UTM UTM and o…

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Q: Use Divergence Theorem to evaluate .v²z²i +z²x²j+x²y²k).ds, where S is the upper part of the sphere…

A: To evaluate the below integral. ∫∫sy2z2i+z2x2j+x2y2kds¯

Q: Let C be the boundary curve counterclockwise of the semidisk x2 + y? < 9,y 2 0. Then f (-2ydx +…

A: Given Information -  C is the boundary curve counterclockwise of the semi disk x2 + y2 ≤ 9 , y ≥ 0…

Q: Let F(x, y, z) = 2z? xi + (y + tan(z))j + (2x²z – 2y²)k. Use the Divergence Theorem to evaluate F.…

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Q: use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the…

A: By divergence theorem

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

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Q: Use a parametrization to find the flux F•n do of F = 5zk across the portion of the sphere

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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(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: Use the Divergence Theorem to find F- ndS, where F = (y°z,x²z,z') and the surface S is the sphere x…

A: See the details solution below

Q: Let S be the sphere of radius 2, oriented inward. Let F = (2x + e", 4y + e*, 2:2). Use the…

A: In the given question we have to solve the double integral s.t∫∫F.ds  to the help of divergence…

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: 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: 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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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.