Multivariable Limit Lesson

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

1. *xy* / (*x*2 + *y*2)
2. *xy*2 / (*x*2 + *y*4)
3. sin(*x*2 + *y*2) / (*x*2 + *y*2)

It turns out that in the first two examples, the limit does not exist, but in the third one it does.