Determine the potential for the field: F = (2y2 + 20e4x-2y, 4xy + 5 - 10e4x-2y)...
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos (1z) – 5z sin (1z)) Do not put the constant "+c" for the potential in your answer below. f(x, y, z) = Submit Answer Tries 0/8 Now calculate 18.di where C is the path ř (t) = (4 cos t, 4 sin t, 3t) for 0 <tsa. The line integral equals
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos (1z) – 5z sin (1x)) Do not put the constant "+c" for the potential in your answer below. f (x, y, z) = -12x*cos(2y)+5z*sin(z) Submit Answer Incorrect. Tries 1/8 Previous Tries Now calculate F. dr where C is the path † (t) = ( 4 cos t, 4 sin t, 3t) for 0 <tst. The line integral equals 0
A flow has a velocity field defined by V={(?2x2?2y2)i+(?4xy)j}, where x and y are in feet. Determine the equation for the equipotential line passing through point (3 ft, 2 ft). Express your answer in the form y2=f(x). If the potential function does not exist, answer "rotational." Express your answer in terms of x.
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the rectangular path from A(0.1) to B(0,3) depicted in Figure 1 Figure 1. Rectangular path of the particle. Compute the work done by the force in this field; Using line integral (if the integral is difficult to evaluate, then use Matlab) b. Also using Green's Theorem without computer aid. Compare your results. a.
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the...
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
(a) [6 marks] Determine the value of coefficient a for which the vector field F = (ayz3 + x2,2x23, 6.xyz2 + 2xz) is irrotational that is VF = 0. (b) [8 marks) Find a potential function for F for the value of the coefficient a determined in item (a). (c) (4 marks] Evaluate the work integral ScF. dr, where is a path running from the origin to the point (3,1,1).
(1 point) Determine whether the vector field is conservative and, if so, find the general potential function. F = (cos z, 2y!}, -x sin z) Q= +c Note: if the vector field is not conservative, write "DNE". (1 point) Show F(x, y) = (8xy + 4)i + (12x+y2 + 2e2y)j is conservative by finding a potential function f for F, and use f to compute SF F. dr, where is the curve given by r(t) = (2 sinº 1)i +...
Consider the vector field F(x, ) (4x3y -6ry3,2rdy - 9x2y +5y*) along the curve C given by r(t)(tsin(rt), 2t +cos(xl)), -2ss 0 To show that F is conservative we need to check a) b) We wish to find a potential for F. Let r,y be that potential, then Use the first component of F to find an expression for ф(x, y)-Po(x,y) + g(y), where ф(x,y) in the form: Differentiate ф(x,y) with respect to y and determine g(y) e Using the...
(1 point) Consider the vector field F(x, y, z) = (2z + 3y)i + (2z + 3x)j + (2y + 2x)k. a) Find a function f such that F = Vf and f(0,0,0) = 0. f(x, y, z) = b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral / F. dr. (1 point) Verify that F = V and evaluate the line integral of F over the given path: F =...