The meaning of bounding curve of a surface

Question

I am reading Stokes Theorem. I am not able to understand the meaning of bounding curve of a surface. What is the definition of boundary curve of a surface $$z=f(x,y)$$ In particular I am trying to figure out the boundary of the portion of the surface $x^2 + y^2 + z^2 =25$ below $z=4$.

Thanks!

Answer 1

There is no boundary for $z = f(x,y)$ unless you specify a domain for $(x,y)$. In your particular example, the boundary is the circle where the plane $z=4$ intersects the sphere $x^2 + y^2 + z^2 = 25$.