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Determine whether or not the vector field is conservative. If it is conservative, find a function...
(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 +...
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...
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)-
Let F(x,y,z) = <2y2z, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative, find a function f such that F = Vf and f(1,2,1)= 8. (b) Using the result of part(a), evaluate the line integral of F along the following curve C from (0, 0, 0) to (3.9, 1.4, 2.6). y2 + x4z3 + 2xy(x3 + y4 + 24)1/3 = K ; K is a constant Answer: Next page
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. (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
6. (4) (a) Is F(x, y, z) = <e'siny, e cosx, esiny > a conservative vector field? Justify. (4) (b) Is F incompressible? Explain. Is it irrotational? Explain. (8) (c) The vector field F(x,y,z)= < 6xy+ e?, 6yx²+zcos(y), sin(y)+xe?> is conservative. Find the potential function f. That is, the function f such that Vf= F. Use a process. Don't guess and check.
(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 is a conservative vector field. F(x, y) =Lye*+cosly))i + lett +xsin(y))}
7. The vector field F =< 3x2z In y + ze+2 +20, - 3y?, x° In y + ce2 +423 > is conservative. Find a potential function f(x, y, z) such that F=Vf. Y