Calculate the flux and the circulation of a vector field Based on the graph, make a conjecture about whether the circulation and flux of F = (– y, x) on %3D C:F(t) = (2 cos(t), 2 sin(t)) for %3D

Q: How do you graph the vector field F = (f(x.y).g(x.y)? Choose the correct answer below. O A. At…

A: Given,  F=<f(x,y),g(x,y)>

Q: 1. Consider the vector field F(r, y) = -y²i+(x+2)j. (a) Evaluate F(0, 1). F(0,1) = (b) Sketch the…

A: Given:

Q: 7. Parallel flow. Sketch and interpret the flow with

A: Given,          Fz=z

Q: A uniform magnetic field B has constant strength b teslas in the z-direction [1.e., B = (0, 0, b) 1…

A: Stoke's theorem ∫CF→.dr→=∫∫S curlF→.dS→ Where S is a smooth surface bounded by a smooth closed curve…

Q: three decimal pI 1.1 ,Yi = i 2.51 X2 = i 1.2 ,Y2 = i 3.273 X3 = i 1.3 Y3 = 4.50283 X4 = i 1.4 Y4 =…

A: Consider the equation

Q: (b) The square with vertices (0,0), (1, 0), (1, 1) and (0, 1), and the vector field F = 3x²yi + x³j.

A:

Q: Let f(x,y) = sin x+sin y. (NOTE: You may use software for any part of this problem.) %3D (a) Plot a…

A: (A) plot the contour of f.

Q: Given the vectors below are a gradient field, sketch 3 level curves of the associated potential…

A: To find the level curves of the given gradient field, for high, medium and low values.

Q: Match the vector field to its graph. 1. 2. = %3D 3. F (x, y) 1 = F (x, y) = F (x, y) 4. E 5.

A:

Q: Find the flux of the constant vector held v=-i-2j+2k through a square plate of area 9 in the…

A: Introduction: Flux is the integral of the dot product of an oriented surface and a vector field. The…

Q: Example Let f(r,y, z) = ryz sin rz. Find Vfo at the point Po = (1, –2, 7) and compute the…

A: to find : (1) grad f. (2) directional derivative.

Q: Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the…

A: Here the given vector field is, v⇀=y2i→+1.1x2j→And dxdt=y2dydt=1.1x2So, dydx=1.1x2y2 Here, ∆t=0.1

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (y -…

A: By using green theorem, we calculate the counterclockwise circulation and outward flux of the given…

Q: Gradient. Directional Derivative Find the directional derivative of f(x, y, z) = 2x2 + 3y2 + z2 at…

A:

Q: b) Find v²f where f = e²x sin2y. cl Write the sufficient condition for ovistence of Lapla

A:

Q: Consider the functions below. F(x, y, z) = xizj+yk r(t) = 4ti + 6t j - t² k (a) Evaluate the line…

A:

Q: Find the gradient vector field Vf of f. f(x, y) = x²-8y Vf(x, y) =

A:

Q: a) Find the Laplace transformation of the function f(t) = cosh at sinh bt

A:

Q: Evaluate the vector-vall function at each giver r(t) = cos(t)i + 3 sin(t)j (a) r(0) = (b) г(π/4)=…

A:

Q: rove that Vx(F)= 0 tor any scalar function

A: Cross product of the scalar function

Q: A particle moves in the positive direction once around the square with vertices (0, 0), (0, 2),(2,…

A: Given, the force field Fx,y=x-sinxi+y2+xj. We have to find the work done.

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.