Question 2 For the following vector fields F determine whether or not they are conservative. For ...
Determine if the following vector fields F: 2 CR" + R" are conservative. In case they are conservative, find a potential function f, that is, such that F= Vf. a) F(1, y) = (x²y, zy), N=R? b) F(1, y, z) = (ze", 22 sin(z), 2+z+1), N=R3 c) F(x,y) = (e cosy, -efsiny), R=R2
(1 point) For each of the following vector fields F decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, Vf = F) with f(0,0) = 0. If it is not conservative, type N. A. F(, y) = (12x - 4y)i + ( 4x + 14y)j f (1,y) = B.FI,y) = 6yi + 7xj f (, y) = (6 sin y)i + (-8y + 6.0 cos y).j...
Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = Vf. (If the vector field is not conservative, enter DNE.) F(x, y, z) = 4xyi + (2x2 + 10yz)j + 5y2k f(x, y, z) =
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-< ye", e + z,y > Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-
(1 point) For each of the following vector fields F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, V f = F) with f(0,0) = 0. If it is not conservative, type N. A. F (x, y) = (-140 – 4y) i + (-4x + 12y)j f (x, y) = B. F (x, y) = -7yi - 6xj f(x,y) = C. F (2, y) =...
7. Determine whether the following vector fields are conservative. If they are, then find a potential function (b) F:cos(),2y, -sin)> 7. Determine whether the following vector fields are conservative. If they are, then find a potential function (b) F:cos(),2y, -sin)>
(1 point) For each of the following vector fields F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, V f = F) with f(0,0) = 0. If it is not conservative, type N. A. F(x, y) = (-14x + 4y)i + (4x + 2y)j f (x, y) = B. F(x, y) = -7yi – 6xj f (x, y) = C. F(x, y) = (-7 sin...
1. (20 points) Identify if the following vector fields are conservative. If there exists a vector field that is conservative, you must also find a potential function for that field. (a) F(x,y,z) = (x3 – xy +z)i + 2 (b) F(x,y,z) = (y+z)i + (x+z)j + (x+y)k (& +y +y-22) i + (- y2)k
(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 +...
4. (16 points) Determine which of the following vector fields is conservative, and construct a potential function for that field. (iii) H(x, y, z) = (y2 +22,22 + 1, 2yz)