Use Lagrange multipliers to find the points on the given cone that are closest to the following point. z2 x2 y2 (2, 4, 0) 1,2,5 X (х, у, 2) (smaller z-value) 0,0,0 (х, у, 2) (larger z-value)

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: f (x, y) = x² + y² – 2x, D is the closed triangular region with vertices (2, 0), (0, 2), and (0, –2)

A: According to the given information, it is required to find the absolute maximum and minimum values…

Q: Use Lagrange multipliers to find the point on the plane x-y+z=7 closest to the point (4,5,1).

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Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: Find the points on the cone z² = x² + y² that are closest to the point (-5,4,0)

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Q: Use Lagrange multipliers to find the points on the cone z2 = x2 + y2 that are closest to (8, 2, 0)…

A: Given: Equation of the cone: z2 = x2 + y2 Given point: (8, 2, 0)   To find: The points on the cone…

Q: Use LaGrange multipliers to find the coordinates of the points on the surface z2 = z² +y² which are…

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Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first oc- tant…

A: We need to find volume.

Q: B) Use Lagrange multipliers to find the points on the ellipse 2x2+y? = 1, where f (r, y) = ry has…

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Q: Use Lagrance Multipliers, and find the point P(r, Y, z) closest to the origin on the plane 2x + y –…

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Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Use Lagrange multipliers to find the points on the given surface that are closest to the origin.…

Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: Find the line of intersection of the given planes. 4x + y-z = 0 and 2x - y + 3z 4 %3D

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Q: Use the method of Lagrange multipliers to find the maximum and minimum values of 2х + у on the…

A: To find : maximum and minimum values of 2x+y on the ellipsoid x2a2+y2b2+z2c2=1, where a, b and c are…

Q: Find the maximum value of f(x, y) = x2y9 for x, y ≥ 0 on the unit circle.

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Q: Use Lagrange's multiplier(s) to find the maximum and minimum for f(x, y, z) = x² + 2x + 2y2 + 3z2 on…

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Q: Determine the convexity/concavity property of the following: (ii) f (x, y) = 2x² – y?

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Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

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Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with…

A: To find the value when the volume is the greatest possible value under the given constraints

Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Given:  The equation of cone is z2=x2+y2. To determine: The points on the given cone that are…

Q: Use Lagrange multipliers to find the shortest distance, d, from the point  (1, 0, −2)  to the plane…

A: Lagrange Method:- The method of Lagrange multipliers is a strategy for finding the local maxima and…

Q: Let a = 3 and b = 3. Find (x, y",z") the closest point from the cone z =V ax²+ by to the point…

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Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e5", where the value ab is as…

A: We need to find the minimum value of ab So, let fx,y=xy We need to minimize this function and find…

Q: 6. Use the Lagrange multiplier method to find the points on the cone z? = x² +y² that are closest to…

A: given the constraint function z2=x2+y2. Use the Lagrange's multiplier method to find the points on…

Q: Use Lagrange multipliers to find the point on the plane  x − 2y + 3z = 6  that is closest to the…

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Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with…

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (-2,2,0)

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Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e9, where the value ab is as…

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Q: Use Lagrange multipliers to Önd the points on the ellipse 2x2+y2 = 1 where f (x, y) = xy has its…

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Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Given data:   The given expression is y2=36+xz.   The expression of the distance of a point from the…

Q: Find the extreme values of z on the surface 2x² + 3y2 + z2 - 12xy + 4xz = 35.(DO NOT USE LAGRANGE…

A: For the solution follow the next steps.

Q: Let S be the sphere of radius 1 centered at (2, 3, 4). Find the distance from S to the plane x + y +…

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Q: Use Lagrange multipliers to find the minimum distance from the Curve Point Parabola: y = x² (0, 3)

A: Given: The parabola y=x2 and indicated point is 0,3 Formula for the distance is d=x1-x22+y1-y22…

Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

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Q: Use the Lagrange multiplier method to find the point of the plane 4x-5y+3z=1 with less distance to…

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Q: Find the minimum distance from the point to the plane x - y + z = 9. (Hint: To simplify the…

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Q: Use Lagrance Multipliers, and find the point P(r, y, 2) closest to the origin n the plane 2r +y-z-5…

A: Given,

Q: Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point…

A: First note that ,          if (x,y,z) be any point on tha plane x-2y + 3z = 6 then distance between…

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

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Q: Use Lagrange multipliers to find the maximum and minimum of f(r, y, z) = -r + 2y + 2z on the ellipse…

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Let the point on the cone is P(x,y,z). The the distance of the point P from the given point…

Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: Use Lagrange multipliers to find the point on the plane x 2y + 3z = 6 that is closest to the point…

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Q: Q6) (Lagrange Multipliers) to the origin Find minimum distance from the surface r? – y – 2? =1

A: The solution is given below in the next step:

Q: 12. Use Lagrange multipliers to find the point(s) on the intersection of the sphere r²+y²+z² = 16…

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Q: Use Lagrange multipliers to find the shortest distance from the point (7, 0, −9) to the plane x + y…

A: The square of distance function is given by fx,y,z=x-72+y2+z+92 and the constraint is…

Q: Use the method of Lagrange multipliers to find the points on the circle x2 + y2 = 52 that are…

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Q: Evaluate //R V2x(y – 2x)dA where R parallelogram on the xy-plane with vertices (0, 0), (0, 1), (2,…

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Q: (a) Use the method of Lagrange multipliers to determine the minimum and maxi values of f(x, y) = x²…

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Q: Let a = 2 and b = 3. Find (x, y ,z) the closest point from the cone z = V ax+by to the point…

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