Chapter 15, Problem 33RE

To determine

To prove: The $\text{curl }F$ of a conservative vector field $F\left(x,y,z\right)=f\left(x,y,z\right)i+g\left(x,y,z\right)j+h\left(x,y,z\right)k$ , $f,g$ and $h$ has continuous first order partial derivatives, in an open spherical region is zero.