Answer
0
Work Step by Step
div $\textbf{F}=\nabla\cdot \textbf{F}=\nabla\cdot\langle e^{x}\sin y,-e^{x}\cos y,z^{2}\rangle$
$=\frac{\partial}{\partial x}(e^{x}\sin y)+\frac{\partial}{\partial y}(-e^{x}\cos y)+\frac{\partial}{\partial z}(z^{2})$
$=e^{x}\sin y+e^{x}\sin y+2z=2(e^{x}\sin y+z)$
Knowing that $(x,y,z)=(3,0,0)$, We get
div $\textbf{F}=2(e^{3}\sin 0+0)=0$
