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Mathematics

Understanding Limits in Multivariable Calculus

Quick fact

A multivariable limit exists only if the function approaches the same value along every possible path to the point, and proving nonexistence can be as simple as finding two different paths that give different limits.

Why this is interesting

In single-variable calculus, a limit is about approaching from the left or right. But what happens when you can approach a point from infinite directions in space?