Use the method of Lagrange multiplier to determine the maximum and minimum values of f(x, y) = x* + 4x – y - on the ellipse x² + 2y² = 4. %3D

Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. (Hint: Use Lagrange multipliers.)

A: Given plane is, 3x+2y+z=6, we need to find the point on this plane closest to the origin.

Q: Using Lagrange multiplier, find the minimum value of f(x,y) = 3x +ly on the circle x2 + y2 = 1. Give…

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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: 7. Derive the orthogonal trajectories of the family of hyperbolas xy = c. %3D

A: The solution are next step

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 minimum and maximum squared distance between the sphere x² + y² + z² = 9 and the point…

A: We have to find the minimum and maximum squared distances between the sphere x2+y2+z2=9 and the…

Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: Q1/ Use Lagrange multipliers to find any maximum or minimum volumes: i) z = f(x,y) = 5 – 3x – 4y and…

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Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: Find minimum distance from the surface x² – y? – z² = 1 (Lagrange Multipliers) to the origin.

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

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Use Lagrange multipliers to find the minimum distance from the plane x+y+z=5  to the point (5,4,4) .…

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Q: Find the minimum of f(x,y) = 3x + 3y on the ellipsoid 3x2 + 3y = 2. Leave your answer correct to two…

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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 orthogonal trajectories of the family of hyperbolas xy = c

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Q: Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

Q: Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci on…

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Q: Find the point on the surface 4x+y-1=0 closest to the point (1,2,-3) using Larange Multipliers.

A: To determine the point on the surface 4x+y-1=0 closest to the point (1,2,-3) The distance from any…

Q: || 9x2 dA, where R is the region bounded by the ellipse 9x2 + 25y2 = 225; x = 5u, y = 3v

A: Here we use transformation to solve this problem.

Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. Hint: Use Lagrange multipliers.

A: The given plane: 3x+2y+z=6 To find the point on the plane 3x+2y+z=6 closest to the origin. Solution:…

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: 4. Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci…

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Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

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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 ellipse 2x +y = 1 where f(x,y) = xy has its extreme values.

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

Q: Maximize xyz on the ellipsoid

A: See the details solution in below

Q: A designer proposed using a paraboloid S,: x² +y² = z as the basis of a container design. However,…

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Q: to find the use lagrange Multiplier Point p (x1s,Z) Closest to the origion on the Plane 2x +y - 2=5…

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Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

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Q: 3. Find the maximum and minimum values of the function f(x, y,z) = x + y+z on the ellipsoid x? +4y²…

A: Given the function is fx,y,z=x+y+z              ...1 and let hx,y,z=x2+4y2+9z2-1764=0…

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: Find the minimum of f(x,y) = 4x + 3y on the ellipsoid 4x2 + 2y2 = 6. %3D Leave your answer correct…

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Q: (a) Where does the normal line to the ellipse x2- x   y + y 2 = 3 at the point (1, -1) intersect the…

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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: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

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Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

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

A: Given,  Plane x + 3y + 4z = 9

Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: 5. Find the orthogonal trajectories of the family of hyperbolas x² - 2y = ax. %3D

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Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: Find the points on the curve of intersection of the ellipsoid x² + 4y² + 4z² = 4 and the plane x –…

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

A: Given: Equation of cone is x2+y2-z2=0 and equation of plane is x+2z=4. To determine: The highest…

Q: Use Lagrange Multipliers to find the absolute maximum value and absolute minimum value of the…

A: We have to find absolute maximum and absolute minimum value for the given function.

Q: Consider the function f(x, y) = xª + y4 – x² – y? – 2xy. | | Determine the maximum and minimum…

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