27. F(x, y, z) = yj – z k, S consists of the paraboloid y = x² + z², 0 < y < 1, and the disk x? + z² < 1, y = 1 %D %3D

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

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Q: 1. The solid bounded by y = 1, y = x², z = 0 and z = y AS A Z-SIMPLE SOLID.

A: Givne that  Solid region y=1,y=x^2,z=0 and z=y  To find the triple integral

Q: 5. . Find sSSzdv where D is the 2 solid bounded by xty'tz=4 and 2= 13x²+ 3y2. (" sce Cueam Come')

A:

Q: d. .2 The solid bounded by the cylinder x+y = 9 and the planes z = 0 and z = 3- x. %3D

A: The solution of the problem is given in the next steps.

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y + 18z on the elipse…

A:

Q: If E is the solid shape bounded by x 2 0,y 20 ,z 2 0 and the plane 2x + 3y +z = 6 evaluate (x + y)…

A: The given question is solved below

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x+ 8y + 12z on the elipse…

A:

Q: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 18. The volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane z = 6

A:

Q: 1. If F= (y,z,x), the outward flux through a smooth closed surface (a) depends on the surface. (b)…

A: Given, F=y,z,x We know,  Flux by the Gauss divergence theorem. ∬F.ds=∬∫divF.dvF=yi+zj+xk If you…

Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

A: Here is the solution of the given problem

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: 5. Evaluate the line integral (r+2y) dr+x² dy where C consists of line segments from (0,0) to (2, 1)…

A: In order to solve this question by the formula of line integral .

Q: 2. Evaluate the triple in tegral where E is the y-2x2+2z20nd the plane y= 8. solid bounded by SI…

A:

Q: Let F = (-z2, 2zx, 4y - x2}, and let C be a simple closed curve in the plane x + y + z = 4 that…

A: Given F={-z2,2zx,4y-x2}. Curve in the plane (s) = x+y+z=4. Area enclosed is 16.

Q: Integrate fcx)9,2) =X+y -Z over thep Poth from OLo.0.0) to A (2,1,2) given by, ostsi (C) = r z i…

A:

Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: Evaluate the triple integral xy dV where E is the solid tetrahedon with vertices (0, 0,0), (6, 0,…

A:

Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

A:

Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: Find a solution to the Dirichlet boundary value problem for a disk. zu 1 du 1 Pu = 0, + -- ar? Osr<…

A:

Q: 43. Find f, 1dS, where s is the portion of the surface deter- mined by z = x2 – V3y that lies above…

A: Find ∫s1 dS where S is the portion of the surface determined by z=x2-3y that lies above the region…

Q: 3. The solid bounded by z = 0, z = 1 – x², z = y and 2y + z = 12.

A: Given that  Region z=0,z=1-x^2 and 2y+z=12  To form a triple integral

Q: A surface x(y, z) is defined implicitly xy + yz +x'z' = 3-xZ Calculate ду

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Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

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Q: Let w=x² +3y² + 2z² where x=rcos, y=rsin 0,z=5t find dw dw ar' at

A:

Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

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 +…

A:

Q: 4. Use Green's Theorem of the Plane to evaluate the following closed path integral. xy2 dx+ 2x2y dy…

A: According to green’s theorem closed path integral over the curve C is calculated by,

Q: 3. Evaluate /// 2* dV if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: triple integral

Q: 5) Evaluate the line integral S YX²dX + XY²dY on curve C, where C is the upper portion of the www m…

A:

Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

A:

Q: (b) || 6xy dV, where E lies under the plane z 1+x + y and above the region in the xy-plane bounded…

A: A triple integral involves the integral with respect to x,y, and z. In this problem, we have to…

Q: 11. Integrate G(x, y, z)=x√y² + 4 over the surface cut from the parabolic cylinder y² + 4z = 16 by…

A:

Q: Evaluate || F-n dS where S is the cylinder (including the disk on the bottom) x² + y² =1 for 0<z<1…

A: First, we plot the given surfaces.Cylinder : x2+y2=1; 0≤z≤1Paraboloid : 3x2+3y2+z = 4; 1≤z≤4.

Q: Solve the problem. 15) Find the centroid of the solid with constant density a enclosed between the…

A: Given :- The centroid of the solid with constant density α enclosed between the sphere of radius 2…

Q: Evaluate the solid bounded by 2x+z=2 and (x-1)2+y2=z.

A:

Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: -4 Evalate SS* dxdy, where D is the region bounded by the hyperbolas xy=2, xy=4 cMd the paraboles…

A: The given integral: Where D is the region bounded by the hyperbolas and parabolas We use change…

Q: Verify Stokes' Theorum for F(x,y,z) = (y,-x,yz) if S is the paraboloid z = x2 + y2 with x2 + y2 = 1,…

A: Given  Fx,y,z=y,-x,yz Then, F→=yi^-xj^+yzk^

Q: 6. Compute the flux of F = [0, 0, z²] through the spherical surface S given as the upper hemisphere…

A: To find- Compute the flux of F→ = 0, 0, z2 through the spherical surface S given as the upper…

Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0

A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.

Q: 6. Evaluate the integral fSSp 4y dV if D is bounded by the elliptic paraboloid z = 3.x?+y²+1 and by…

A: Application of integration

Q: Example 6: Evaluate ez dz dy dx E Where E is enclosed by the paraboloid Z = 3+ x? + y² , the…

A: The given problem is to evaluate the given triple integral of given function ez for which region E…

Q: E is the region behind the surface y = 4 – x² that is in front of the region in the xy-plane bounded…

A: Given integral: ∫∬E18x dV Given that E is the region behind the surface y=4-x2 that is in front of…

Q: c, y, z) = x²zi + xz'j+ y ln(x + 1) k, s the surface of the solid bounded by the 2z = 4, y = 3, x =…

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Q: 2. Suppose that the edge lengths r, y, and z of a closed rectangular box are changing at the…

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Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

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Q: 2) Use a change of variables to evaluate , zdV; where Dis bounded by the paraboloid z = 16 – x - 4y?…

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Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

A: