Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse that is formed by the intersection of the cylinder x? +y² = 16 and the plane y+ z = 4

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: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y-2)² = 2x -2, S4: x = 0, S5: y =…

A: To find- The Solid bounded by the surfaces S1 : 2x + 3z = 6, S2 : y = 2, S3 : y - 22 = 2x - 2, S4 :…

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Q: 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the…

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Q: Find the minimum distance from the point to the plane x - y + z = 3.

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Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

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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: 39.) The solid bounded by the cylinder x+y² = 9 and the planes z= 0 and z = 3 - x. 40

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Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

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Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and 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: The surface area of the solid generated by revolving the straight line 2y = x+1 bounded by x-1, x 3…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 9x + 18y + 27z on the elipse…

A: Using Lagrange Multipliers with Two Constraints to find the maximum and minimum values of the given…

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

A: Lagrange's multiplier method uses the system of the equations obtained from the partial derivatives.…

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: 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: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

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Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

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Q: 3 Find the abscissa of the centroid of the region between the parabola y = 9 − x2 and the line y…

A: Given :The parabola y=9-x2 and the line y=2-2x from x=0 to x=2.To find :The abscissa of the centroid…

Q: The path C is a line segment of length 13 in the plane starting at (4,5). For f(x,y)=5x+12y,…

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Q: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

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Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

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Q: The solid bounded by the surfaces S1: −2 (z - 2) = y2 S2: x = 5 - 2z S3: x = 0 S4: y = 0 S5: z = 0…

A: Given that, A solid is bound by the surfaces, S1: -2(z-2)=y2S2: x=5-2zS3: x=0S4: y=0S5: z=0

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Q: The value of the integral (inage 1). where C is the closed curve 4x2 + 5y2= 7, 3x + 2y − 9z = 5.

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Q: about the line x = -2 ソ=2× ソ=2° 1 2

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Q: ây _ở: x>0, t> 0 where y (0, t) = 1, y (x, 0) = 0. Find the bounded solution of

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

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

A: Volume of a solid is obtained using triple integration by the formulae =∫∫∫dx dy dz The solid is…

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Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

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Q: (b) Let F = (-yx², xy²). Let D be the annulus 1 < a2 + y² < 4, and let C be its boundary. Evaluate

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Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y − 2) 2 = 2x − 2, S4: x = 0, S5:…

A: Consider the surfaces  S1: 2x + 3z = 6, S2: y = 2S3: (y − 2)2=2x − 2, S4: x = 0S5: y = 0S6: z = 0

Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

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Q: Find the abscissa of the centroid of the region between the parabola y = 6 − x2 and the line y = 1 −…

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Q: Find the centroid of the region bounded by the graphs of the equations using any method y = √(1 −…

A: Consider the given equations y=fx=1-x2y=gx=0 First, find the point of intersection of the given…

Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

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Q: The solid bounded by the surfaces S : -2(: – 2) = y² S2 : 1 = 5– 2y S3: r=0 S4 : y = 0 Ss : z = 0…

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Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

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