Find the greatest and smallest values that the function f(x,y) = 4xy takes on the ellipse x +2y² = 1 by using the Method of Lagrange Multipliers.

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 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: At what points does the curve r(t) = t i + (6t - t2)k intersect the paraboloid z = x2 + y2? (Enter…

A: Given: Equation of curve:                                    r(t)=t i +(6t-t2) k Equation of…

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

A: The solution are next step

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

A:

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

A:

Q: Find the dimensions of the largest rectangular box in the first octant (x, y, z > 0) with one corner…

A:

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

A:

Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Use Lagrange multipliers to find the points on the given surface that are closest to the origin.…

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: SET UP the necessary equations to find the point on the intersection of the surfaces x2 + 4y2 + 4z2…

A: The solution are next step

Q: Find the orthogonal trajectories of the family of curves r² + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

A:

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A:

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

A:

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: 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: Let f(x, y)=sqrt(2x²+4y² +8) -x. The domain of c for which the level curve f(x, y) = c is an ellipse…

A:

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 points on the surface z2 = xy + 4 closest to the origin.

A:

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

A: We have to find the best quadratic approximation Q(x,y) for (x,y) near (0,0).

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 equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

A:

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: Calculate | [(a* – 3y) dæ + (2y³ + 4x) dy] wherein y(t) = (3cos(t), 3sin(t)), 0 <t < 2ñ, is an…

A: Please check step 2 for the solution.!

Q: Which of the following is the orthogonal trajectories of the family of ellipses 2x² + y² = a? xy = C…

A:

Q: Find a parameterization for the hyperbolic paraboloid z = z – y².

A:

Q: Find the value of ∫∫s(x^2y^2z^2)dS correct to four decimal places, where S is the part of the…

A:

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

A:

Q: Find the minimum of f(x,y) = 5x + 2y on the ellipsoid 9x2 + 2y2 = 7. Leave your answer correct to…

A:

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

A:

Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

A:

Q: Obtain the Solution x, y > 0, xy > 1 of 1 the PDE Ury Such that x+y 2у и 3 0, их on the hyperbola…

A: 1st we set up the initial value condition and draw the figure than set up PDE and solve it

Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Given data:   The given expression is y2=36+xz.   The expression of the distance of a point from the…

Q: Q4/Find the abs.max and abs.min valuse of the huctu f,y) = \+xy-3x on the cosol regen oounded by the…

A:

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 points on the curve x^2+xy+y^2=16 which one nearest and farthest from the origin using…

A: Let us consider the given function f(x,y) Subjected to g(x,y)=C Solving using Lagrange's multipliers…

Q: Find the minimum of f(x,y) = 4x + 5y on the ellipsoid 9x2 + ly2 = 7. Leave your answer correct to…

A:

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

A: Topic = Geometry

Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

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

A:

Q: Find the maximum and minimum valves of f(xy)=5x+Y on the ellipse X+36y=!

A:

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

A:

Q: Let f(x, y)=sqrt(2x²+4y² +8) -x. The domain of c for which the level curve f(x, y) = c is an ellipse

A:

Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

A:

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

A:

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x²+ y²+ z²= e2x

A: Solution: Given equation is x^2+y^2+z^2=e^(2x)

Q: Let f(x, y) =V2x²+4y2 +32 -x. The domain of c for which the level curve f(x, y)=c is an ellipse is

A: For the solution follow the next step.

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

A: