Use the method of Lagrange multipliers to find the maximum of the func- tion f(x, y) = x² + xy+y² on the unit circle a² + y² = 1. %3D

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 maximum point of y = x + x a. (2,-2) b. (1,2) c. (-1,-2) d. (2,3)

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Q: Find the maximal value of the function f(x,y)=2x3-y3 on the circle of equation x2+y2=7.

A: We have to find the maximal value of the function  on the circle of equation

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 Lagrange multipliers to find the points on the sphere ² + x² + y² − 2y − 10 = 0 closest to and…

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Q: A grass fire burns in an approximate circle. Firefighters, spraying the fire, can affect the area of…

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Q: Calculate (4x² + Se) dy, where C is the triangle of vertices (0,0), (2,0) and (2,2). [(4x²+ Note:…

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Q: Consumer A’s utility function is UA(x1,x2)=min(2x1,x2). Consumer B’s utility function is…

A: Given that - Consumer A’s utility function is UA(x1,x2)=min(2x1,x2). Consumer B’s utility function…

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

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Q: Find the orthogonal trajectories of the family of 2 curves x² + y² = cy A B Ⓒ с D none of the…

A: Given curve x2+y2=cy

Q: A missile is launched with a constant thrust corresponding to an acceleration of "a" ft/sec². The…

A: Given: The height of the missile after time "t" seconds is ft,a=12a-40t2, where a ft/sec2 is the…

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 point/s on the parabola y = 3x2 that is/are…

A: Let's find closest point to (0,3).

Q: Use Lagrange multipliers to find the shortest distance from the point (5, 0, −8) to the plane x + y…

A: The plane equation is :x+y+z=1The point is :P(5,0,-8)The aim is to find the Shortest distance from…