4. Use the method of Lagrange Multipliers to find the point on the plane r+y- 2 = 5 that is closest to the point (-3, 5, 4).

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: Use Lagrange multipliers to find the distance from the point (3, 0, -1) to the plane 6x - 4y + 7z +…

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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: Find the point(s) of intersection of the line x = 1 – t, y = t, z =1– 2t - and the paraboloid z = 8…

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Q: Use the method of Lagrange multiplier to determine the maximum and minimum values of f(x, y) = x* +…

A: Local Maximum and Minimum by using lagranges Multiplayer.

Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

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 area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

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

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Q: Find the point closest to origin in R³ that is on both the planes 3x+y+z=5 and x+y+z=1.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Show that the area of that portion of the surface of the paraboloid x² + y² = 4z included between…

A: Here we need to find area between given plane and x*x + y*y = 4z

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

A:

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

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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: 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: (a) Use the method of Lagrange multipliers to find all candidates of the point(s) on the surface x2…

A: Lagrange multiplier.

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

A:

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

A: Let (x,y,z) be the point which is closest to the point (2,4,0) .

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

A:

Q: Use the method of Lagrange multipliers to find the shortest distance from the point (-2, –3, 1) to…

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Q: A. Show that the planes (x+y- z = 1) and ( 2x - 3y + 4z = 5 ) are neither parallel nor…

A: Let's find.

Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

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Q: Use the Lagrange multiplier method to find the point on the plane 4x +3y +2z = 0 with the smallest…

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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: 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: 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: Find the distance between the given parallel planes. 4x – 5y + z = 16, 8x – 10y + 2z = 3

A:

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: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

Q: 3. Use LaGrange multipliers to find the point on the plane 2r - y+4z = 10 that is closest to the…

A: Use Lagrange method to find point

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

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

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Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

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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: Use LaGrange multipliers to find the minimum distance between the origin and the plane x+2y+3z=28.

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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: By using the Lagrange multiplier, find the point on the plane 2x + py – qz = r which is closest to…

A: We have to find point on the given plane which is closest to the origin by using the Langrages…

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 distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0. %3D

A: Distance between parallel planes d=(d2-d1) /(sqrt(a2+b2+c2)

Q: Find the point on the circle x2 + y2 = 1 that is closest to the point (1, 3/4) by using the method…

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Q: to Rind the points Lagrange multiplier surface (x-1)(y-2)(Z-)=| near est Qz use on the to the point…

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

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Q: Use the method of Lagrange multipliers to maximize 2x + 3y – 4 on the circle x² + y? = 13

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Q: and V is the dosed by the Planes x=0, y=O, ニこ

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Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

A: According to the given information, it is required to find a point lying on the intersection of the…