Set up and compute the surface area of the part of the surface $z=x^2-y^2$ which is inside the cylinder $x^2+y^2=9$.
Compute the surface area of the part of the surface $z=y^2$ about the triangle with vertices $(0,1,0)$, $(1,0,0)$, and $(1,1,0)$.
Compute the surface area of the part of the plane
$\frac xa+\frac yb +\frac zc=1$
(where $a\gt 0$, $b\gt 0$, and $c\gt 0$)
in the first octant ($x\gt 0$, $y\geq 0$, and $z\geq 0$). Hint: Start by determining where the plane intersects the $x$, $y$ and $z$ axes.