For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, $\nabla f = \mathbf{F}$). If it is not conservative, type N.

A. $\mathbf{F} \left( x, y \right) = \left( -10 x + 1 y \right) \mathbf{i} + \left( 1 x + 4 y \right) \mathbf{j}$
$f \left( x, y \right) =$

B. $\mathbf{F} \left( x, y \right) = -5 y \mathbf{i} - 4 x \mathbf{j}$
$f \left( x, y \right) =$

C. $\mathbf{F} \left( x, y, z \right) = -5 x \mathbf{i} - 4 y \mathbf{j} + \mathbf{k}$
$f \left( x, y, z \right) =$

D. $\mathbf{F} \left( x, y \right) = \left( -5 \sin y \right) \mathbf{i} + \left( 2 y - 5 x \cos y \right) \mathbf{j}$
$f \left( x, y \right) =$

E. $\mathbf{F} \left( x, y, z \right) = -5 x^{2} \mathbf{i} + 1 y^{2} \mathbf{j} + 2 z^{2} \mathbf{k}$
$f \left( x, y, z \right) =$

Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"