Math 3298 - Hampton - Lab 4 - Due 10/2

Continuity of 2D scalar functions.

Exercise

1.  Investigate the behavior of the family of functions (x^n + y^m)/(x^(2p) + A*y^(2q)) where n,m,p,q are positive integers and A is a constant.  For what values of these parameters can the function be extended continuously to (0,0)?  Explain and justify any answers you find.  (This material is mostly covered in Chapter 13.2.)

Manipulate[Plot3D[(x^n+y^m)/(x^(2*p)+A*y^(2*q)),{x,-1,1},{y,-1,1},PlotPoints->100,Mesh->False],{{n,3},1,10,1},{{m,4},1,10,1},{{p,2},1,10,1},{q,1,10,1},{{A,1},-1,1}]