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Limits — Approaching Without Arriving

Behavior near a point, not only at it · BC Calculus · greeting

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Owl · Picture walking toward a glass door that slides open only when you get close — but for this thought experiment, you never quite step through. Still, people watching can say where you're heading. A limit is that "heading" language for functions. It describes how outputs behave as inputs approach a value, not necessarily what the function returns if you plug the value in. On the board: a delivery-drone altitude that follows a nice formula everywhere except at the warehouse gate x = 3, where the log skips a reading. Left and right tables still settle toward the same height. So — if the function is undefined at a point, does that automatically kill the limit?

Owl: Picture walking toward a glass door that slides open only when you get close — but for this thought experiment, you never quite step through. Still, people watching can say where you're heading. A limit is that "heading" language for functions. It describes how outputs behave as inputs approach a value, not necessarily what the function returns if you plug the value in. On the board: a delivery-drone altitude that follows a nice formula everywhere except at the warehouse gate x = 3, where the log skips a reading. Left and right tables still settle toward the same height. So — if the function is undefined at a point, does that automatically kill the limit?

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