Chapter 14.4, Problem 48ES

Determine whether the statement is true or false. Explain your answer.

Suppose that $z=f\left(x,y\right)$ has continuous first partial derivatives in the interior of a region R in the $xy\text{-plane},$ and set $\text{q}=〈1,0,\partial z/\partial x〉\text{and}\text{r}=〈0,1,\partial z/\partial y〉.$ Then the surface area of the surface $z=f\left(x,y\right)$ over R is

${\displaystyle \underset{R}{\iint }‖\text{q}\times \text{r}‖}dA$