Answer to Question #260101 in Calculus for tarie

Question

) If F(x, y, z) = e xˆi + yzˆj − yz2ˆk, find the divergence of F at (0, 2, −1)

Answer 1

If $F(x, y, z) = e^x\cdot i + yz\cdot j − yz^2\cdot k$, let us find the divergence of $F$ at $(0, 2, −1).$

It follows that

$Div\ [F(x,y,z)]=\frac{\partial( e^x)}{\partial x} +\frac{\partial(yz)}{\partial y} +\frac{\partial(-yz^2)}{\partial z} =e^x+z-2yz,$

and hence

$Div\ [F(0,2,-1)]=e^0-1-2\cdot 2(-1)=4.$

Answer: the divergence of $F$ at $(0, 2, −1)$ is equal to 4.