Teach & case
Help a near-peer reason through the idea — when you explain it, you understand it best — then read the real decision it comes from.
Help Vela with the limit
What you've shown you can teach
A real case · you decide
Vela and the speed-camera instant
Vela — a student contesting a speed-camera ticket that claims an exact speed "at the instant" of the flash
The ticket says Vela's car was doing 70 km/h "at the instant" the camera flashed. But speed is distance ÷ time — and over an instant, time is zero. Distance ÷ 0? That's undefined. So how can a speed "at an instant" even mean anything?
Vela computes average speed over shorter and shorter windows around the flash: over 2 seconds, 68.4; over 1 second, 69.2; over 0.1 s, 69.9; over 0.01 s, 69.99…
The exact instant itself is still 0 ÷ 0 — genuinely undefined. But the averages don't wander; they home in on a single number. That approached value is what "instantaneous speed" means.
At the exact instant, the formula is 0 ÷ 0. So is the instantaneous speed simply undefined?
Vela's friend graphs a different function with a literal HOLE at x = 2 (undefined there). Does it have a limit as x → 2?
Vela's argument isn't that the camera is wrong — it's that "speed at an instant" is a LIMIT, and the limit is a clean 70. That's Vela's whole thing: the value a function approaches, not the value it happens to hit.