3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid z = x? + 4y? and the point (3,0,0).

Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

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: 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: 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: 6 Consider points P and Q in the x-y plane, with P = (1,0) and Q (0,1). The line integral %3D %3D Q…

A: Introduction :Given, two points P and Q .P= (1,0)Q= (0,1)We have asked for the line integral of

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: Use the method of Lagrange multipliers to find the maximum of the func- tion f(x, y) = x² + xy+y² on…

A: Find the maximum of the function fx,y=x2+xy+y2 on the unit circle x2+y2=1 using the method of…

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 the method of Lagrange multipliers to find the minimum and maximum values of the function f (x,…

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Q: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid z = x²…

A: (3)Let (x,y,z) lies on parabolaThe distance d=x-32+y2+z2such that z=x2+4y2Lagrabge multiplier…

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 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: 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: Let T(x, y, z) = 100 + x2 + y2 represent the temperature at each point on the sphere x2 + y2 + z2 =…

A: solutionGivenT(x,y,z)=100+x2+y2x2+y2+z2=30plane x=2

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: 2. Let f: R? → R be the function which satisfies for all (x, y) € R² that f (x, y) = xy. Use the…

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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 and minimum outputs for the function f (x,y) = xy – y² on the portion of the disk…

A: The given function is f(x,y)=xy-y2    ....(1) Let g(x,y)=x2+y2-1=0    ....(2) h(x,y)=x+y-1=0…

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: Find the absolute maximum and minimum values of f(x, y) = 3xy−6x−3y + 7 on the closed triangular…

A: Find out the absolute maximum and minimum values of  f(x,y)=3xy-6x-3y+7 for the maximum and minimum…

Q: Find the minimum distance between origin and the plane 3x + 2y+z=14 O a. 2y2 O b. 3/2 O C. V14 O d.…

A:

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: Let T(x, y, z) = 100 + x2 + y2 represent the temperature at each point on the sphere x2 + y2 + z2 =…

A: Given: Tx,y,z=100+x2+y2 represent the temperature at each point on the spherex2+y2+z2=40. To Find:…

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: 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…

A:

Q: et T(x, y, z)= 100+ x² + y² represent the temperature at each point on the sphere x² + y² + z² = 80.…

A: Given: Tx,y,z=100+x2+y2sphere g= x2+y2+z2=80plane h =x-z=0

Q: Let P be the plane 2x + y – z = 2 and let Q(1,0,3) be a point. We want to find the minimum distance…

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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: Use the method of Lagrange multipliers to minimize f (xy) =x² +y² on the hyperbola x-y=1.

A: Given: fx,y=x2+y2 and xy=1

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: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

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: For x,y,z > 0, use the Lagrange Multiplier Method to find the minimum value of 1 1 1 + + x y Subject…

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

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Q: Q1/ Find maximum,minimum OULE ,and saddle point of the surface Z = x³y³ - 12x + 3y + 12.

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

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Q: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid 2= z +…

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Q: Use the method of Lagrange multipliers to find the absolute extrema of the function f(x, y, z) = x +…

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Q: Solve the boundary-value problem by method of separation of variables: du Su +3 Sy = 2u, given u (x,…

A: A

Q: Q2/ Examine the following surface for maximum , minimum, and saddle points z = x3 – 3x2 – 4y² + 2

A: Take the first order and second-order partial derivatives of z with respect to x and y.

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

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Q: 4) Let h(x, y) = 2x² + y² – 2x²y. Find the absolute minimum and maximum values of the surface on the…

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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: 1. Using the lagrange multiplier method, find the maximum and minimum temptaure of he plate whose…

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