Use Lagrange multipliers to find the minimum and maximum values of f (x, y) = 3x − 2y on the circle x^2 + y^2 = 4.

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: To find the minimum distance from the given curve to the point using Lagrange multipliers method.…

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

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Q: Find the minimum distance from the point (2, -1, 1) to the plane x + y - z = 2.

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Q: Find the minimum and maximum squared distance between the sphere x² + y² + z² = 9 and the point…

A: We have to find the minimum and maximum squared distances between the sphere x2+y2+z2=9 and the…

Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: What is the maximum vertical distance between the line y = x + 51 and the parabola y= x² over the…

A: Given: The line y=x+51 and the parabola y=x2 To find: Maximum vertical distance between given line…

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: Suppose the point (x,y) on the line x+y=3 is nearest to the point (0,0). That is distance d between…

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

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Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

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Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

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Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A: Use Lagrange multiplies we find heighest point on the curve ofintersection of the surface cone:…

Q: Find the minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

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Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

Q: Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

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Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

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Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: Given surface plane: x+y+z=1 Point (8,1,1).

Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated poi…

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Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

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Q: Find the minimum and maximum distances between the sphere r²+y²+z² = 9 and the point (2, 3, 4).…

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Q: Find minimum perpendecular distance between given paraboles. y = x2 + 1 y = x - x2

A: To find the minimum distance between 2 parabolas

Q: Find the minimum distance from the parabola x − y2 = 0 to the point (0,3) Minimum distance =

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Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: Topic = Application of derivative

Q: Draw the region in the xy plane where x + 2y ::; 6, 2x + y ::; 6, x 2 0, y 2 0. It has four corners.…

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Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: Q/ Find the points have minimum distance from the origin to the surface. xyz²=1

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: What is the maximum vertical distance between the line y = x + 38 and the parabola y = interval [–…

A: Given line equation is y=x+38 Given parabola equation is y=x2 From the above two equations x2-x-38=0…

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…