By using the Lagrange multiplier, find the point on the plane 2x + py – qz = r which is closest to the origin. (b) P: 9 q=5 r=2

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

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Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

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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: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Evaluate the hutergral sss of dV, where F= (x²-2)i + 208; - 22k and V is the dosed the Planes x=0,…

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Q: Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

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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: Below the paraboloid z = 18 – 2x² – 2y² and above the xy-plane -

A: The region D lies below the paraboloids z=18-2x2-2y2 and above the xy-plane.

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x 3y + z = -2.

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Q: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

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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: The orthogonal trajectories to the family of hyperbolas xy= C is given by the family 1)y=cx 2)y2 -x2…

A: We need to find the orthogonal trajectory to the family of hyperbola xy=c

Q: Find the greatest and smallest values that the function f(x,y) = 4xy takes on the ellipse x +2y² = 1…

A: Let's find.

Q: Use the Lagrange multiplier method to find the maxima and minima of the function f(x, y) = xy on the…

A: Consider the given function fx,y=xy and let gx,y=3x2+y2-6. Using Lagrange multipliers,…

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

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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: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

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: Use the method of Lagrange multiplier to find the largest and least values of h(x, y) = x2y on the…

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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: Find the distance between the planes – 3x + 5y = 32 and – 3x + 5y = 27.

A: Simply use the formula for the distance between two planes.

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

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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: 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 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 best quadratic approximation, Q(r, y) of V9 – 6x – 4y for (r, y) (0,0). near

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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 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: 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 parametrizations for the line in which the planes 3r- 6y – 2z = 3, and 2x+y-2z = 2 intersect.

A: Given Equation of planes 3x-6y-2z=3 and 2x+y-2z=2

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

A: This question is related to Lagrange multipliers theorem. We will solve this question by using…

Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

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: 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: a) Evaluate //(-ri-yj+2: k) n dS, where a is the portion of the paraboloid : = 3r - 3y between the…

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