Summary: for a conservative field curl of field should be zero.
(1 point) For each of the following vector fields F decide whether it is conservative or...
(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 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) =...
(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) = (-6x - y)i + (-x + 14y)j f (x, y) = B. F(x, y) = -3yi – 2xj f (x, y) = C. F(x, y) = (-3 sin...
Only the Matlab part !!! Question 2 For the following vector fields F determine whether or not they are conservative. For the conservative vector fields, construct a potential field f (i.e. a scalar field f with Vf - F) (a) F(z, y)(ryy,) (b) F(z, y)-(e-y, y-z) (c) F(r, y,z) (ry.y -2, 22-) (d) F(x, y, z)=(-, sin(zz),2, y-rsin(x:) Provide both your "by hand" calculations alongside the MATLAB output to show your tests for the whether they are conservative, and to...
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
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF=...
(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 +...
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
Problem 7. Given that each of the following vector fields F is conservative Find a potential function f such that f = F and evaluate fe F dr along the given curve C 1. F(r,y) y C: F(t)(t3- 2t, t3 + 2t), 0 <t<1 2. F(x,y, ) yze"* i + e#* j + xye k C: F(t)(t2 1)i +(2 -1)( -2t)k, 0t 2
please help ! Q1-Q6 1. Let F (3x - 4y +22)i+(4x +2y 3z2)j + (2xz moving once around an 4y zk be a vector field. Consider a particle ellipse C given by parametrization r= 4 cos ti +3 sin tj. Find the work done. 3 3 = 3, y=-- and 2 1 2. Let D be the region in the first quadrant bounded by the lines y=-r1, y 4 + 1. Use the transformation u 3 2y, v r +...