Calculus › Section N · Functions of several variables › Topic N.2
Limits and continuity in several variables
In the plane a point can be approached from infinitely many directions, and a limit must survive them all. This one change makes limits subtler — and continuity richer — than anything one variable prepared you for.
In this topic
- From two directions to infinitely many
- Neighbourhoods and regions
- The definition of a limit
- The limit laws carry over
- Worked example: a limit by substitution
- Worked example: a squeeze proof
- The two-path test
- Two paths are never enough
- Continuity in several variables
- Worked example: testing continuity
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP