Multivariate Limits

Limits on multivariable functions.

Recall with single variable limits, it depends on what direction you approach the point for a limit. But with multivariable functions, there are infinitely many directions we can approach from.

In general, the direction we approach the limit point can determine the limit value. The limit only exists if the limit is path-independent.

We only focus on surfaces that are smooth enough such that the limit exists. Both in MATH 119, and in real, physical representations.