## Calculus 8th Edition

(a) Let us consider that $F=Pi+Qj$, then we have $divF=\dfrac{∂P}{∂x}+\dfrac{∂Q}{∂y}$ we can see that when $\dfrac{∂P}{∂x}$ is positive, since the $x$ components of the vectors increases in length, as we move along the positive $x-direction$ and $\dfrac{∂Q}{∂y}$, is positive, since the $y$ components of the vectors increases in length, as we move along the positive $y-direction$. This yields that the divergence is positive. (b) Let us consider that $F=Pi+Qj$, then we have $divF=\dfrac{∂P}{∂x}+\dfrac{∂Q}{∂y}$ This implies that $curlF=(\dfrac{∂Q}{∂x}-\dfrac{∂P}{∂y})k=(0-0)k=0$ Hence, $curlF$ is zero.