Multivariable Limit Lesson

thingiverse

These models represent each a multivariable function f(x,y), for which f(0,0) is undefined. Nonetheless, each case prompts the inquiry of whether or not the limit of f(x,y) as (x,y) approaches (0,0) exists. The three functions from these models are xy / (x2 + y2), xy2 / (x2 + y4), and sin(x2 + y2) / (x2 + y2). It turns out that in the first two examples, the limit does not exist, but in the third one it certainly does.