Find the maximum value of f(x,y,z)=2x+5y+13z on the sphere x²+y²+z²=36

Q: Find the maximum value of f(x,y,z)=15x+y+6z on the sphere x²+y²+z²=441

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Q: Find the maximum and minimum values of ƒ(x, y, z) = x - 2y + 5z on the sphere x2 + y2 + z2 = 30.

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Q: Find the maximum value that ƒ(x, y, z) = x2 + 2y - z2 can have on the line of intersection of the…

A: Given and planes are

Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

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Q: Find the maximum and the minimum values of f(x.y.z) = 9x- 9y +2z on the sphere x +y +z = 166.

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Q: Find the maximum value of f(x,y,z)=D24x+18y+21z on the sphere x²+y2+z²=D49 256.324

A: Given query is to find the max value for f.

Q: Find the maximum value of f(x, y) = 3ry(9 – 45x – 9y) over the triangle with vertices (0,0), (,0)…

A: Maximum value occurs at critical points or on the boundaries of the triangle.

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

A: Use Lagrange multiplies we find heighest point on the curve ofintersection of the surface cone:…

Q: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

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Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

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Q: Find the orthogonal trajectories on the sphere x2 + y2 + z2 = a2 of its intersection with the…

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Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

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

A: Using Lagrange Multipliers with Two Constraints

Q: Find the maximum value of f(x, y) = 11zy(9 – 99x – 9y) over the triangle with vertices (0, 0). (†,0)…

A: Given: The triangle vertices are (0,0),(111,0) and (0,1) f(x,y)=11xy(9-99x-9y)…

Q: Find the points on the sphere x2+y +z = 109 where f(x,y,z) = 6x + 8y + 3z has its maximum and…

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Q: Integrate F = 3x2yi + (x3 + 1)j + 9z2k around the circle cut from the sphere x2 + y2 + z2 = 9 by the…

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Q: Find all point on the plane x+ yt z= 5 in the first octant at which f(x, y,z) xy'z' has a maximum…

A: We have to find all points on the plane x+y+z=5 in the first octant at which fx,y,z=xy2z2 has a…

Q: Find the points on the sphere x +y +z = 154 where f(x,y,z) = 3x + 8y + 9z has its maximum and…

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Q: Find and classify all the critical points of the surface with its equation z = 32°y – y° + 3z – 3y²…

A: Given: z = 3x2y - y3 + 3x2 -3y2 + 2

Q: Find the absolute maximum and minimum of f(x,y)= 4xy^2 - (x^2)(y^2) - xy^3 on the closed triangular…

A: f(x,y)=4xy2-x2y2-xy3fx=4y2-2xy2-y3fx=04y2-2xy2-y3=04-2x-y=0…

Q: (a) Show that the two surfaces S₁: z = xy and S₂ : z = ³x² - y² intersect perpendicularly at the…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: Find the area of the upper portion of the cylinder x2 + z2 = 1 that lies between the planes x = ±1/2…

A: Find the area of the upper portion of the cylinder x2 + z2 = 1 thatlies between the planes x = ±1/2…

Q: 4. What is the maximum value of f(x, y, z) = xyz for points (x, y, z) lying on the ellipsoid x² + 4…

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Q: B) Determine the parametrizations of the untrimmed surfaces S1, S2 and S3 without constraints(free)…

A: Given: Surfaces S1: 2x-4y+z=4 S2: 2y=6-x S3: x2=16-4z To find: Parametrization of the surfaces S1,…

Q: Find the average height of the paraboloid z = x2 + y2 over the square 0<= x <= 2, 0…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Consider M is the mass of the triangular plate bounded by the y-axis and both the lines. To find…

Q: Find the surface which intersects the surfaces of the system z(x+ y) =c(3z+1) orthogonally and…

A: To finding the surface which is intersecting given system and orthogonal to circle is given as…

Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…

A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…

Q: Find the maximum value of  f(x,y,z)=27x+7y+3z on the sphere x2+y2+z2=81

A: For this question we will use Lagrange multipliers where f(x,y,z)=given function and…

Q: Find the maximum value of f(x,y,z)=25x+3y+17z on the sphere x2+y2+z²=100

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Q: Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2…

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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 %3D as if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = 4-x-y lying above…

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Q: Find the maximum value of f(x,y,z)=9x+15y+9z on the sphere x2+y2+z²=100

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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 area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: Find the maximum value of f(x,y,z)=24x+18y+21z on the sphere x²+y²+z²=49 I

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Q: Find out the nature of the surfaces 2x +3y² +z² –8x+6y-4z-3=0 and compute their centers and lengths…

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Q: The minimum value of f(x,y,z) = x^2 -2y + 2z^2 on the sphere x^2 + y^2 + z^2 =1 is ....?

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Q: Maximize 2x + 3y+ 5z on the sphere x +y +z=19.

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Q: Find the absolute maximum and absolute minimum of the function f (x, y, z) = x³ + 2y along the curve…

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Q: Find the maximum value of f(x,y,z)=9x+14y+29z on the sphere x2+y2+z²=25

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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: Find the average height of the (single) 34. Average height of a cone cone z = Vx² + y² above the…

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Q: 2 : Use Lagrange multipliers method to show that the maximum value of f(x, y, z) = x²y²z² on the…

A: In lagrange method, the Critical points are the points that cancel the first order partial…

Q: Find the points on the surface z²2=xy+1 that are closest to the origin using LaGrange multipliers

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Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…