Multivariable Limit Lesson by stepanp21

Last crawled date: 5 years, 4 months ago

These models each represent a multivariable function f(x,y) for which f(0,0) is undefined. However, in each case, one can ask the question 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)
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 does.