Questão 2 Check thatF(x, y) = (ez+y – y2 – cos(y))i + (ez+y – 2yx + xsen(y))j is a conservative field and find a potential function. Use this potential function to Ainda não calculate respondida F- drwhere Cis the parabola y = x?connecting to the pointA(2, 4)to the point B(0,0). Vale 2,00 ponto(s). P Marcar questão 圖 Parágrafo В I

Q: 2) Let F= 2 xyi + (x² + 2) j. find a potential function, f, for it. Show that Fis conservative and

A:

Q: Verify that f (x, y, z) = xy + yz 2 is a potential function for the vector field F = (y, x + z2,…

A: Given: Vector field F→=y , x+z2, 2yz To verify that fx , y, z=xy+zy2 is the potential function.

Q: Suppose the slope field given below is for the equation u' = f(t, u). Draw a possible solution for…

A:

Q: !

A: We have to find

Q: F(1, y, 2) = (2c" cos(3y), –3e²" sin(3y) + VV:). a. Find divF(x, Y, 2) and curlF(x, y, z). b. Based…

A: This is a problem of multi-variable calculus.

Q: 3 , find a potential function for the vector field F by inspection or show that one does not exist.…

A:

Q: Compute dr where C is the ellipse 4x² + 2 = 4 (with counterclockwise 32 motion) and F(x, y) = (2++²…

A: Given Information:The vector field is given as .Ellipse equation:  with the counterclockwise…

Q: a) Calculate the line integral of the vector field F(x, y) = yi − 5xj from the point (0, 3) to the…

A:

Q: A piston of diameter 84 mm is being manufactured for an automobile engine. What is an approximation…

A:

Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F = sin 8y i + cos 2x…

A:

Q: Find the work done by the force field F(x, y) = x sin(y) i + yj on a particle that moves along the…

A:

Q: K Find the work required to move an object in the force field F= (x,3) along the straight line from…

A: Given force field isF = < x , 3 >We have to check whether the given force field F is…

Q: (iv) Find the work done by the force field F(x, y) = x²i+ yeªj on a particle that moves along the…

A:

Q: y +3z x + 2z 2y + 3x Consider the conservative vector field F(x, y, z) = with domain R³. Find a…

A:

Q: 6. Find the circulation of the field F(x, y) = -yi + x²j along the closed elliptical path x² + = 1…

A:

Q: Use Green's Theorem to evaluate(¹-28) O-96 O-75 O 105 -2y) de- (62-4ry") dy where C' is shown below

A: We want to calculate the integral ∫Cy4-2ydx-6x-4xy3dy

Q: 1. Show that the field F = (x + cos a)i+ (K +4 – y sin y)j + (2³ + K – 9)k is conservative and find…

A:

Q: Show that the vector field 1 F(x, y, z) = (- :)= (-2: 25³ sinh (2y − 1) - x²y is conservative by…

A: If a vector field F→(x, y, z) is conservative then there exists a potential function f(x, y, z) such…

Q: EX 3! Show that F (x₁y) = (2xy - 3) + " + (2y + x² ) 5* is conservative and find a potential of it..

A: Use the partial derivative for finding the potential function

Q: 19. Find potential function for = (3xy, æ³)

A:

Q: Find the gradient vector field of f(x, y) = x° sin(9y). F(x, y) = x°i+ sin(9y)j F(x, y) = 9x°…

A: