4. What is the maximum value of f(x, y, z) = xyz for points (x, y, z) lying on the ellipsoid x² + 4 + = 16?

Q: 3. Find the maximum and minimum values of the function f (x, y, z) = x+ y + z on the ellipsoid x2 +…

A: Given we have given a function  f(x, y, z) = x+y+z we have to find the maximum and minimum value of…

Q: Integrate H(x, y, z) = x2sqrt(5 - 4z), over the parabolic dome z = 1 - x2 - y2, z>=0.

A:

Q: 1) Find the vdlemes of the oolids generated by revolving the resion in the first quuadrant bounded…

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Q: Find a point on the hyperboloid x2 + 4y2 – z2 = 1 where the tangent plane is parallel to the plane x…

A: Given  and plane

Q: Integrate G(x, y, z) = xyz over the surface of the cube cut from the first octant by the planes x =…

A: Here, the surface is in the first octant. Therefore, the integration 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: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

A:

Q: 39.) The solid bounded by the cylinder x+y² = 9 and the planes z= 0 and z = 3 - x. 40

A:

Q: Q. No. 4 Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y =…

A: Given lines are, y=x and y=2-x

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 extreme values of ƒ(x, y, z) = x( y + z) on the curve of intersection of the right circular…

A:

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

A:

Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

A: Here is the solution of the given problem

Q: 17. Integrate G(x, y, z) = xyz over the triangular surface with vertices (1, 0, 0), (0, 2, 0), and…

A:

Q: The solid bounded by the paraboloids 2= - 8+z²+ y² and z -3-32²-3y² has volume:

A:

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: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z² 24 and the paraboloid…

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: 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: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

A:

Q: 2 Find the surface area of the portion of the cone x² + y² = 2² above the region inside the…

A: we have to find the surface area of the portion of the cone x2+y2=z2 above the region inside the…

Q: Find the volume of a right circular cylinder of radius a = 4.00 with a paraboloid of revolution…

A:

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: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: Find the maximum and minimum values of the function f(x,y, z) = x + y + z on the ellipsoid x² + 4y²…

A: To determine the maximum and minimum value of the function fx,y,z, subject to the constraint…

Q: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

A:

Q: 17. Find the area of one side of the "winding wall" standing orthogonally on the curve x = y°, 0 < y…

A:

Q: 1_2 Can you please help me with this example in a step by step guide. Thank you very much!!

A: To calculate the coordinates (x,y,z) and also define the absolute extremum for the provided surface…

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

A: To find the minimum distance between 2 parabolas

Q: (B) Integrate paraboloid (x, y, z)=- 2x-²-2-0 by the plane x=1. over the surface cut from the end of…

A:

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

A:

Q: A point moves along the intersection of the elliptic paraboloid z = 6r + 7y and the plane y = 2. At…

A: Given: A point moves along the intersection of the elliptic paraboloid z = 6x2 + 7y2 and the plane y…

Q: 16. The solid within the spherex² + y² + z² = 9, outside the cone z = Vx2 + y², and above the…

A:

Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…

A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…

Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 4y and the plane y = 4. At…

A:

Q: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

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Q: Find the points on surface z^2=xy+4 closest to origin.

A:

Q: 5) Find the region in the xy-plane for which (sin x – y)y' = vx- y satisfies the nonlinear existence…

A: A differential equation  y' =f(x,y) will have at least one solution in the region where f(x,y) is…

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

A:

Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y − 2) 2 = 2x − 2, S4: x = 0, S5:…

A: Consider the surfaces  S1: 2x + 3z = 6, S2: y = 2S3: (y − 2)2=2x − 2, S4: x = 0S5: y = 0S6: z = 0

Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

A:

Q: Suppose that the Celsius temperature at the point (x,y,z) on the sphere x +y +z =1 is T= 1600xyz“.…

A: This is a problem related to maxima and minima. Based on the general formula we will answer the…

Q: 5) Consider the surfaces S1 : ryz = 10 and S2 : z =r² + y and the %3D point Po = (1,2,5).

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: Let h(x, y) = 2x² – 2x²y + y². Find the absolute minimum and maximum values of the surface on the…

A: We use partial derivative to find critical points to check maximum and minimum value

Q: 4) Let h(x, y) = 2x² + y² – 2x²y. Find the absolute minimum and maximum values of the surface on the…

A:

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

A: