Dominic and Edward want to investigate a differentiable function Q (2, v) and its level set at height 4: Q(a, v) - 4. (1) a) By differentiating both sides of the equation above with respect to and using the chain rule, they obtain the equation, S(z, v) + T(z,v) 0. (2) Dominic and Edward find that the function S(z, y) is: (choose the correct formula) and also agree that the function T(1,v) is: (choose the correct formula) Dz dy b) Suppose now that S and T are differentiable. To help Dominic and Edward, complete the sentence below. The first order differential equation (2) is Click far List because (choose the best option). as as as O Sand T are polynomials. O as O Qis a palynomial. c) Dominic has already found a function Q(z, y) satisfying the conditions in (a) above, and says it's now not necessary to check the condition you gave in (b) to determine whether or not (1) is exact. Edward disagrees and says that Dominic must still check your condition in (b) to determine whether or not (1) is exact. Who is right? O Edward is comect O Dominic is correct
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.
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