Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0) and give the corresponding minimum distance.

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: Find the maximum value of f(x,y,z)=2x+5y+13z on the sphere x²+y²+z²=36

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Q: Find the maximum value that ƒ(x, y, z) = x2 + 2y - z2 can have on the line of intersection of the…

A: Given and planes are

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

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Q: Sketch the surfaces CYLINDERS z = y2 - 1

A: We need to sketch the surface formed by the function

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x+ 8y + 12z on the elipse…

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

A: perpendicular distance

Q: Find the points on the surface x2 - zy = 4 closest to the origin.

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Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

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Q: find the absolute minimum and maximum of f(x,y)=2x^3+y^4  over the disk x2+y2 ≤ 1

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

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Q: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

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Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: 1/ Find maximum,minimum Z= x³y³-12x + 3y + 12. ,and saddle point of the surface

A: Use the method of Lagrange multipliers to find maxima minima of the given function as in next step.

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: Find all point on the plane x+ yt z= 5 in the first octant at which f(x, y,z) xy'z' has a maximum…

A: We have to find all points on the plane x+y+z=5 in the first octant at which fx,y,z=xy2z2 has a…

Q: Find the points on the sphere x +y +z = 154 where f(x,y,z) = 3x + 8y + 9z has its maximum and…

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Q: Find and classify all the critical points of the surface with its equation z = 32°y – y° + 3z – 3y²…

A: Given: z = 3x2y - y3 + 3x2 -3y2 + 2

Q: Find the absolute maximum value of the function f(x, y) = 3x² + 2y² – 4y+1 | on the disk which has…

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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: (a) Show that the two surfaces S₁: z = xy and S₂ : z = ³x² - y² intersect perpendicularly at the…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: Find and classify all the critical points of the surface with its equation z = 3x"y + y* – 3x2 – 3y?…

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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: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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

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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: Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

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Q: Find the minimum of f(x,y) = 4x + 3y on the ellipsoid 4x2 + 2y2 = 6. %3D Leave your answer correct…

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Q: Find the maximum value of f(x,y,z)=25x+3y+17z on the sphere x2+y2+z²=100

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Q: Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2…

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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: 5) Let R(x, y) = 3x² + y². Find the minimum value of R on the hyperbola xy 2.

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

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

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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 surface area of the rotating object from the curve y = x^2 with the constraint 0 ≤ x ≤ 1…

A: The formula for the surface area of the rotating object from the curve y=f(x) with the constraint…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0< x <1…

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Q: Find the maximum value of f(x,y,z)=9x+14y+29z on the sphere x2+y2+z²=25

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Q: Find and classify all the critical points of the surface with its equation 2 = 3a²y + y3 – 3x² – 3y?…

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Q: Find the distance between the point P(1, 1, 1) and the surface x² + 2y² + 3x² = 1.

A: Given Point P1, 1, 1 and surface x2+2y2+3z2=1

Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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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: Graph the surface 1 = y2 + z2 –- by first sketching at least three cross sections in each of the xy…

A: We have to sketch the graph of the following surface in the 3D space: . First we have to sketch the…

Q: Find the minimum distance from the point (0, 0, 4) to the surface  z = (1-2x-2y)^1/2   (Round your…

A: Solution:

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…

Q: Find the points on the surface xy – z2 = 1 that are closed to the origin.

A: Given surface is xy-z2=1. let xy-z2-1=0⇒z2-xy+1=0 Now distance from origin is…