Find the highest and lowest point (x, y, z) along the surface 8x +10y+ 4xy – x² – 2yʻ within the region of R (-5, 10), (-5, 0), and (5, 0). Z =

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: Find the surface area for the portion of the surface f(x,y)=1-x² + y that lies above the triangular…

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Q: Find [[fw ryz dV if W is the solid region in R³ below the surface z = x² + y² and above the square 0…

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Q: Integrate f(x, y, z) = 20xz over the region in the first octant (x, y, z 2 0) above the parabolic…

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Q: Integrate G(x, y, z) = xyz over the surface of the cube cut from the first octant by the planes x =…

A: Here, the surface is in the first octant. Therefore, the integration is

Q: (a) Integrate g(x,y,z) = Inx+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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

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Q: Integrate G(x, y, z)=x4 y ( y2 + z2 ) over the surface of the cylinder y2 +z2 = 25 that lies in the…

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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: Find the average height of the paraboloid z = x+y over the square 0sxs1, 0 sys1. The average height…

A: Here in this problem we are given                                      z=x2+y2  ,0≤x≤1 and 0≤y≤1We…

Q: I need help finding the absolute maximum and minimum values of f on the set D.

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Q: Find the area of the surface of the paraboloid f(x, y) = 2 − x2 − y2 Paraboloid that lies above the…

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Q: find Ix, Iy, I0, x, and y for the lamina bounded by the graphs of the equations. y = 0, y = 2, x =…

A: The value of I0,Ix,Iy.

Q: Find the area of the surface.The part of the surface 2y + 4z − x2 = 5 that lies above the triangle…

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Q: F = (x² – y²,x, 2yz); C is the boundary of the plane z = 6 – 2x – y in the first octant.

A: Given, F=x2-y2,x,2yz Find the line integral ∮CF·dr in the following. Here C is the boundary of the…

Q: Integrate G(x, y, z) = y + z over the surface of the wedge in the first octant bounded by the…

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Q: Find the centroid of the region in the plane enclosed by the curves y = +-(1 - x2)^(-1/2) and the…

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Q: Find the average height of the paraboloid z = x + y over the square 0sxs2,0sys2. The average height…

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Q: Find the area of the part of the surface z = x² + 2y that lies above the triangle with vertices…

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Q: Determine the centroid, C(X,9.2). of the solid formed in the first octant bounded by z+y- 16 = 0 and…

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Q: Given the curve x = 2 y – y´ and the line x = 0 Find the ordinate of the centroid y of the region…

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Q: Find the area of surface x2 – 2y – 2z = 0 that  lies above the triangle bounded by the lines x = 2,…

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Q: 4. Find the area of the surface S where S is the part of the plane z = 3x +y that lies above the…

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Q: Find the centroid of the surface cut from the cylinder y2 + z2 = 9, z>= 0, by the planes x = 0…

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Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

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Q: a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: 3. Find the centroid of the region bounded by the parabola y? = 4x, the y-axis, and the line y = 4.

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Q: y 1 X 1 2.

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Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

A: According to the given information, it is required to find the area of the surface.

Q: É = ( 2x3 + y°, y3 + z³, 3y²z), S is the surface of the solid bounded by the paraboloid z = 1– x2 –…

A: We will find out the required flux.

Q: Integrate g(x, y, z) = x4y(y2 + z2 ) over the portion of the cylinder y2 + z2 = 25 that lies in the…

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Q: Find the centroid of the region that is bounded below by the x-axis and above by the ellipse (x2/9)…

A: As shown in the figure the ellipse is bounded below by x-axis.It is clear from the symmetry that the…

Q: =valuate the double integral [2aydA, 2xy dA, where D is the triangular region with vertices (0,0),…

A: Given that a double integration and given  D is  triangular region with vertices (0,0) (1,2) and…

Q: Find the centroid of a thin, flat plate covering the “triangular” region in the first quadrant…

A: Consider the given curve.

Q: Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1 < x < 3, 0 < y < 1.

A: Given surface is z=f(x,y)=1+2x+3y+4y2 where f(x,y)=1+2x+3y+4y2 Differentiate f(x,y) partially with…

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: Find the centroid of the region between the parabola x + y2 - 2y = 0 and the line x + 2y = 0 in the…

A: Given equation of parabola is, Given equation of line is,

Q: Integrate G(x, y, z) = x2y2 + 4 over the surface cut from the parabolic cylinder y2 + 4z = 16 by the…

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Q: 2y do over the surface S: z = ; 0<x< 2, 0<y<3 Evaluate

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Q: y. y:3x- 31 to

A: Consider the figure, which is given below

Q: Use the transformation (change of variables) x = 2u +v and y = u+ 2v to set up the integral / (x –…

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Q: (a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

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Q: Let h(x, y) = 2x² – 2x²y + y². Find the absolute minimum and maximum values of the surface on the…

A: We use partial derivative to find critical points to check maximum and minimum value

Q: Find a parametrization for the intersection of the surfaces: z = x2 + y2 and  x2 + 4y2 = 1

A: Find the parametric representation for the intersection of the given surfaces.

Q: integrate the given function over the given surface. H(x, y, z) = x2√(5 - 4z), over the…

A: Application of integration: We can use cylindrical coordinate to find a parametric equation for the…

Q: Integrate G(x, y, z) = x + y + z over the surface of the cube cut from the first octant by the…

A: Definition used:

Q: Find the value of a if the centroid of the region bounded by the parabola y² = 4px and the line = a…

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