Math 3298 - Hampton - Lab 3 - Due 9/27

Lab reports should conform to the guidelines explained on the handout.  Collaboration during the lab is strongly encouraged, although the write-up of the lab report must be done individually.

Continuity of 2D scalar functions.

Exercise

1.  Investigate the behavior of the family of functions (x^n + y^m)/(x^p + A*y^q) 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.

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