1. The problem statement, all variables and given/known data Describe the level surfaces of f(x,y,z) = z + sqrt(x^2 + y^2) 3. The attempt at a solution First of all, what is actually a level surface? Just a normal surface in space? I followed an example I found on the internet, and this is my attempt at a solution: First replace f(x,y,z) with a constant k = z + sqrt(x^2 + y^2) Then square (k is now another constant) k = z^2 + x^2 + y^2 This is an ellipsoid, so the level surfaces are ellipsoids centered at the origin. Is this the right solution? If so, is it possible to say more about the ellipsoids?