The paradox of the derivative | Essence of calculus, chapter 2

Derivatives center on the idea of change in an instant, but change happens across time while an instant consists of just one moment. How does that work?
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Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative.


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