Discontinuity Surfaces

cults3d

I use these models to demonstrate surfaces that feature a nonremovable discontinuity at the origin in my Multivariable Calculus classes. The Infinity Surface is defined by the equation z = y/(x^2 + y^2). Limits of 0, infinity, and negative infinity are encountered when approaching (0,0). The Pinched Surface has the equation z = 2xy/(x^2 + y^2). At the point (0,0), I find limits of 0, 1, and -1. These visualizations were created using Mathematica.