Find the volume of the solid bound between the paraboloid z = x^2 + y^2 and the plane x + z = 0 as follows. (a) Find an equation describing the projection of the intersection of the plane and the paraboloid in the xy-plane. What is the shape of the curve described by the equation?

Q: Find the equation of the tangent line to the trace y-3 of the quardic surface defined by 9x² + 2y²…

A: We have to find the equation of the tangent line to the trace y=3 of the quardic surface defined by…

Q: Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent…

A: at point (1, 2, 5)at point (1, 2, 5)

Q: Determine the centroid of the following Fig from X and Y axes. Y, 30 centT1 2 CentQ1 -4 -3 -2 -1 1 2…

A:

Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

A:

Q: arameterize the intersection of the plane x = 1 and the surface z = x2 - 2x2y + y2.

A: To parameterize the intersection of the plane x = 1 and the surfacez=x2−2x2y+y2, we can set x = 1 in…

Q: let C be the curve of intersection of the 3-D graph of x2=2y (a "parobolic cylinder") with the graph…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.