A surface S has a parametrization ¤(u, v), whose domain D is the square shown in the figure. Suppose that has the following normal vectors N(B) = (1,5,0) N(D) = (4,0, 1) N(A) = (4, 1,0) N(C) = (6,0, 1) Estimate s f(x, y, z) dS, where ƒ is a function such that f(0(u, v)) = u + v. (Use decimal notation. Give your answer to three decimal places.)

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.