V = (x +y) z, evaluate ∮ VdS, where S is the surface of the cylindrical wedge defined             by 0 < ϕ < π/2, 0

Q: 15. If the surface S has projection R on the xy-plane, show that F.īdS = S da dy ה.F provided |ñ -…

A: Question: If the surface S has projection R on the xy-plane, show that ∬SF¯·n¯dS=∬RF¯·n¯dxdyn¯·k¯…

Q: If (a,ß.r) is a point at which the surface x2+y2-z-2x+42=0 has a horizontal tangent plane, then Iyl=

A: Horizontal tangent plane

Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

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Q: Find fff y av, y dV, where E is the solid bounded by the parabolic cylinder z = ² and the planes y =…

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Q: If f (0)=f'(2), find the difference c-2d for the following cubic spline S(x) with clamped boundary…

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Q: The surface of many airfoils can be described with an equation of the form xa₁x y ‚ = + 0 = ₂2 [²₁…

A: You can find matlab code and answer for this problem in next step

Q: Below is the solid Q bounded by the surfaces S,: x? +y? +z? = 4, S;: z = V3 and S,: y= x in the…

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Q: 8. (x – y) dV, where E is enclosed by the surfaces z = x² – 1, z = 1 – x² , y = 0, and y = 2 E

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Q: The attached figure shows the surface S1: y + z= 2, limited in the first octant with surface S2: x =…

A: The area of a surface z=f(x,y) bounded by the region R is given by the integral expression:-…

Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = x° and the planes y = 0 and z…

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Q: 3. Evaluate , (x + z)dS where the surface S is the first-octant portion of the cylinder y² + z² = 9…

A: Step:- 1 Since, we know Surface integrals ∫∫Sf(x,y,z)dS=∫∫Df(x,θ) rx×rθ dxdθ…

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: Compute 3xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: Given a surface 3xy - In (4z – 3) = 0, where z = decimal places. f(x,y). Find zx at y = -6, z = 1.…

A: We have given  3xy - ln(4z - 3) = 0             3xy= ln(4z-3)             4z-3= e3xy…

Q: Evaluate ſ[ſp z dV where E lies between the spheres x² + y² + z² = 1 and + y*¨+ 2² = 4 in the first…

A: Solution:

Q: Evaluate ez dV where E is enclosed by the paraboloid z = 4 + x? + y², the cylinder x? + y? = 1, and…

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Q: Given the surfaces S1:x2+y2=a2 and  S2: z =a2−y2 with a ∈ R not zero and arbitrary, its intersection…

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Q: Verify Green's theorem for Q7 [x(x? + y²)dx – y(3x² – y²)]dy Where C is the boundary of the triangle…

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Q: Use Stokes' theorem to evaluate ∮C z2ex^2 dx + xy2dy + tan− 1 (y)dz where C is the circumference x2…

A: Application of Stokes Theorem:

Q: Evaluate xy dV where E is bounded by the parabolic cylinders y = x², x = y² E and the planes z = 0…

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Q: Given a surface 2xy - In (3z- 2) = 10, wherez=f(x, y). Find zx at y =7, z= 1. Leave your answer…

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Q: If V = (x +y) z, evaluate ∮ ? ??, where S is the surface of the cylindrical wedge defined by 0 < ϕ <…

A: Consider the given information. V=x+yz and the given limits are 0&lt;ϕ&lt;π2, 0&lt;z&lt;2. Convert…

Q: Evaluate fF.ndS, where F-4xi-2y' j+z'k and S is the surface bounding the region x' +y' =4, and the…

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Q: Find /// y dV, where E is the solid bounded by the parabolic cylinder z = 2 and the planes y = 0 and…

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Q: Find vdv y dV, where E is the solid bounded by the parabolic cylinder z = x and the planes y = 0 and…

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Q: If E is the solid shape bounded by x 20,y 20,z 20 and the plane 6x + 4y + 3z = 12 evaluate %3D (y +…

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Q: 2. Evaluate ([.(Vx F). ds, where S is the surface of the paraboloid x2 + y2 + z = 4 above the…

A: We have given F→=(x2+y-4)i+3xyj+(2xz+z2)ksurface is given x2+y2+z=4 and above the xy planediagram of…

Q: In exercises 13-18, compute the surface area of the surface obtained by revolving the given curve…

A: Solving part (b) as requested. Given:

Q: ded above by surface z = 10 – x2, bou e planes y = 0 and y = 3.

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Q: Find // y dV, where E is the solid bounded by the parabolic cylinder z = x? and E the planes y O and…

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Q: 1 Evaluate dV, where E lines between the spheres a? + y? + z² = 25 and %3D x² + y? + z2 49 in the…

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Q: Without using the formula (Gauss), calculate E∫∇.F(x)dx where  F(x) = x32k, E :x12+x22≤ x3, 0≤x3≤1…

A: We are asked to find the integral ∫E∇·Fxdx where Fx=x32k^, dx=dx1dx2dx3 and E is the solid bounded…

Q: 10/ Compute e Fids, where S is the surface z =N16-x²-y² oriented up ward and F = <y,-x, zZ %3D 工=?

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Q: 1 Evaluate dV, where E lies between the spheres x2 + y2 + z2 = 9 and x2 + y? + z2 x2 + y? + z2 36 in…

A: we want to find the triple integral ∫∫∫E1x2+y2+z2  dVwhere E lies between the sphere x2+y2+z2=9  and…

Q: In each of the following cases, draw each solid Q bounded by the surfaces whose equations are given…

A: To graph the below surface that is in the first octant. x2=−z−3z=2y+z=3

Q: Consider the surface given by x2 + y? + z? = a². Show that every normal line to this surface passes…

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Q: Given a surface 3xy - In (3z - 2) = -5, where z = f(x,y). Find zx at y = 3, z = 1. Leave your answer…

A: This question is based on Partial differentiation of function

Q: Evaluate the surface integral. ∬Sz2dS,S∬Sz2dS,S is the part of the paraboloid x=y2+z2x=y2+z2 given…

A: Evaluate the surface integral. ∬Sz2dS,Sis the part of the paraboloid x=y2+z2 given by 0≤x≤4

Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = = 2 and the planes y = 0 E and…

A: The solution is given below

Q: Here is a problem where it is challenging to even figure out what the surface looks like. Consider…

A: The solution is in step 2 with clear information and step by step wise.

Q: S y = 3 – 2 4z – 4 = 3(x +1)?

A: Let us start solving the problem step by step

Q: Given that the total flux across the surface, S of the tetrahedron bounded by the planes x=0, y=0.…

A: To draw graphs in 3d we need to find intersections with co ordinate axes and also with co ordinate…

Q: Evaluate (x + 5y) dV where E is bounded by the parabolic cylinder y = x² and the planes z = 3x, y =…

A: given is  a partial differential equation in dX , dY, dZ we can partially integrate the given…

Q: The measurements x1 = 10m, x2 = 8m, and x3 = 6m represent the sides of a rectangular parallelepiped…

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Q: Compute 5xy ds, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: The surface area of the part of z = 2+ /4 – x² – y? that lies inside the paraboloid z = x² + y? is

A: Given is the equation of a surface and a paraboloid. The objective is to find the surface area. The…

Q: calculate ∫ ∫ ∫Ty dv, being the T region inside the paraboloid z= 1/(x2+y2)the sphere x2+y2+z2=5

A: We need to calculate the triple integral ∫ ∫ ∫Ty dv, where T being the region inside the paraboloid…

Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = a and the planes y = 0 and z =…

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