Calculus I Unit One: Limits

Calculus I Unit One: Limits Limits describe where a function is heading.

Not where it lands — where it approaches. We care about behavior near a point, not just at it.

That matters when functions have holes or weird behavior. Limits let us talk about motion at

an instant. They’re the reason derivatives exist. For example: lim x→2 (x²)

As x gets closer to 2 — like 1.9, 1.99, 2.01 — x squared gets closer

to 4. So even if we never plug in 2, the limit is 4. That’s the idea

of a limit.