Answer
$u=xy$ and $v=\dfrac{y}{x}$
Work Step by Step
The region $R$ can be defined as:
$\dfrac{1}{x} \lt y \lt \dfrac{4}{x}, x\lt y \lt 4x$
when $x \gt 0$ and $y \gt 0$, then we get
$1 \lt xy \lt 4$ and $1\lt \dfrac{y}{x} \lt 4$
Plug $u=xy$ and $v=\dfrac{y}{x}$
Now, we have
$1 \lt u \lt 4; 1\lt v \lt 4$
Hence, $u=xy$ and $v=\dfrac{y}{x}$
