I can’t figure them out. Pls help
In: Mathematics
Consider y=1/x. Simple math can tell us that no matter how large of a value we use for x, y will never equal zero.
But, we could say that, “as x approaches infinity, y approaches zero”. That’s pretty much what a limit statement sounds like out loud. We know it’ll never be zero, but that’s where that function is always headed, closer and closer to zero.
These are important because they let mathematicians work with infinitely small or infinitely large intervals and series. That leads to things like derivatives.
Imagine a curved line, and wanting to measure its “curvature” or its “rate of change”. You could hold a ruler across two points of that curve, and you might get a kind-of-sort-of idea of it. You might get a decent approximation of it, even. Now use two points that are closer to each other. Now use two points that are even closer. And closer. And closer.
See a pattern? If you “could” get infinitely close to a single point, and form a line that represents the precise “instantaneous” rate of change of the curve you’re measuring, you’d need a concept like a limit. If you were able to put a formula to calculate the rate of change of your original function for a given value, you’d have a derivative.
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