## Parametrized Surface

For a parametrized surface r: K (subset of R^2) -> R^3 and a parameter value (u0,v0) in K, show that there is a neighborhood N of (u0,v0) such that r(N) is the image of a projectionally parametrized surface. A projectionally parametrized surface is one that has as its image the graph of a function defined on a region in a coordinate plance. Ex: r(x, y) = (x, y, g(x,y)) where g: R -> R is continuously differentiable with bounded partial derivatives.