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Q: Since it involves limits, is calculus always an approximation?

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For those of you unfamiliar with calculus, what follows is day 1. In order to find the slope of a curve at a particular point requires limits, which always feel a little incomplete. At every step there’s always a little farther to go, but “in the limit” there isn’t. If there are N rectangles they’ll each be wide and will be tall (just so you can double-check, in the picture N=6). In mathspeak, the total area of these rectangles isThe fact that is just one of those math things.