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

What is an "instantaneous rate of change" when change happens across time?

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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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