Calculus is about slicing things (like time, distance and area) up into smaller and smaller pieces, until those pieces are infinitesimally small, and being able to use those infinitesimally small pieces to make extremely precise calculations. For example, when we say a car travels at 100 km per hour, we can start by measuring the 100 km distance the car traveled in one hour, but that doesn’t tell us how fast the car was travelling at any particular point in its journey unless we assume a single uniform speed (and real systems simply don’t work that way). If we take two measurements – one at 30 min and another at 60 min – we can now understand how fast the car traveled on average during each half of it’s trip. Maybe it was 90 km per hour for the first 1/2 hour, and 110 km hour for the second half, so overall it would be 100 km per hour. Now we have more precise information. We can take measurements at 4 intervals, or 8 or 16 or 32, etc., with each measurement getting closer and closer to knowing the speed of the car at any particular instant. Taking this to its extreme (but logical) conclusion, we can determine the speed of the car at every instant through calculus, and it turns out this process gives us a lot of very useful information and insights about how things work in the real world (including how the speed is changing at any particular moment).

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