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

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

A:

Q: Find the maximum value of f(x,y,z)=15x+y+6z on the sphere x²+y²+z²=441

A:

Q: Find the maximum and minimum values of ƒ(x, y, z) = x - 2y + 5z on the sphere x2 + y2 + z2 = 30.

A:

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

A:

Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

A: Given surface is 9x2+4y2=30 and plane is  9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

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: 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 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 maximum and the minimum values of f(x.y.z) = 9x- 9y +2z on the sphere x +y +z = 166.

A:

Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y + 18z on the elipse…

A:

Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

A:

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

A:

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

A:

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: Find the area of one side of the “wall” standing orthogonally on the curve 2x + 3y = 6, 0<=x<=…

A: To Determine: Find the area of one side of the “wall” standing orthogonally on the curve…

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: Integrate G(x, y, z) = xyz over the triangular surface with vertices (1,0, 0), (0, 2, 0), and (0, 1,…

A: To Determine: integrate Gx,y,z=xyz over the triangular surface with vertices (1,0,0),(0,2,0) and…

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

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

A:

Q: Find the orthogonal trajectories on the sphere x2 + y2 + z2 = a2 of its intersection with the…

A:

Q: Find the points on the sphere x2+y +z = 109 where f(x,y,z) = 6x + 8y + 3z has its maximum and…

A:

Q: Integrate F = 3x2yi + (x3 + 1)j + 9z2k around the circle cut from the sphere x2 + y2 + z2 = 9 by the…

A:

Q: Find the area of the part of the surface z = x² + 2y that lies above the triangle with vertices…

A:

Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

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 maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes and…

A:

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

A:

Q: Bounded by the cylinders z = 2x2, y = x² and the planes z = 0, y = 4

A:

Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

A:

Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

A:

Q: 4. What is the maximum value of f(x, y, z) = xyz for points (x, y, z) lying on the ellipsoid x² + 4…

A:

Q: B) Determine the parametrizations of the untrimmed surfaces S1, S2 and S3 without constraints(free)…

A: Given: Surfaces S1: 2x-4y+z=4 S2: 2y=6-x S3: x2=16-4z To find: Parametrization of the surfaces S1,…

Q: Find the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).

A: To find the minimum distance first write distance function. Which is the square distance from  .

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

A:

Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance

Q: Find the maximum value of f(x,y,z)=24x+18y+21z on the sphere x²+y²+z²=49 I

A:

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 ....?

A:

Q: Maximize 2x + 3y+ 5z on the sphere x +y +z=19.

A:

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

A:

Q: Find the average height of the (single) 34. Average height of a cone cone z = Vx² + y² above the…

A:

Q: 2 : Use Lagrange multipliers method to show that the maximum value of f(x, y, z) = x²y²z² on the…

A: In lagrange method, the Critical points are the points that cancel the first order partial…

Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

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: Find a parametrization for the intersection of the surfaces: z = x2 + y2 and  x2 + 4y2 = 1

A: Find the parametric representation for the intersection of the given surfaces.

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: he maximum value of f(x, y, z) = 4x + 2y

A: Here we have to find the maximum value of f(x, y, z) = 4x + 2y − 8z .......... (A) on the sphere x2…