1. Let a, b and c be 1, 1 and 9 respectively Consider the ellipsoid & given by the equations + = 1. a² 62 c² (a) Let P₁ = (±x, ±y, ±z) be the vertices of a rectangle inscribed in E. Explain why the volume of & is given by V = 8xyz. (b) Use the method of Lagrange multipliers to determine the largest possible volume of E.

Q: Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area x?…

A:

Q: 4. A 3D solid has base that sits in the x-y coordinate plane. That base is a triangle with vertices…

A: Integrating the equation of curve under certain limit gives the value of area between curve and axis…

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

A:

Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

A:

Q: Find the area of the surface. The part of the cylinder y² + z² = 9 that lies above the rectangle…

A:

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: We have to find the volume of the largest rectangular box in the first octant with three faces in…

Q: The cylinder x² + y² = 25 intersects the plane x + z = 5 in an ellipse. Find the point on such an…

A: Given:The cylinder is: .The plane is .The cylinder intersects the plane in an ellipse.

Q: Solve for the centroid coordinate

A: Solve for the centroid coordinate

Q: 2 Find the volume of the ellipsoid 2y 7z 16

A: Volume of the ellipsoid for the equation,

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: Given that  Plane x+7y+10z=70  To find the largest volume

Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: Find the volume of the solid formed if we rotate the ellipse+ = 1 about the line 4x + 3y = 20.

A: Calculation of Volume.

Q: QUESTION 3 If /= [0,4], calculate the norm p of the following partition P= {0, 1, 1.5, 2, 3.4, 4}

A: