Find the surface ara of the sphere that lies inside the paraboloid , using cylindrical co-ords.
What I've done:
equations of the sphere and paraboloid in cylindrical co-ordinates are and .
substituting and rearranging these gives
this gives the points of intersections
And that's as far as I can get. I'm having a problem with the partial derivatives.
To get them I've done this:
When I differentiate, am I right in assuming the 'z' on the RHS disappears as well? Does it go to 1 or 0?