Limits and Continuity

The limit and continuity of functions of multivariate functions is more complex than its partial derivative since we need to consider all the variables at one time.

Limits

We also use the ${\displaystyle \delta -ϵ}$ definition to define the limit of multivariate functions. We will not talk about it here.

• Polynomial functions always have their limits.
• Rational functions have their limits if and only if their denominator is not ${\displaystyle 0}$.

Continuity

Interior and Boundary