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I think as a corollary you can say when you are taking an antiderivative or definate integral, you are also taking limits.

And the bizarre thing for me, is all the applications of those. Like, when you are finding the arc length of a smooth curve, you are taking a limit. When you aer finding volume, you are taking a limit.

Can someone explain to me how you are taking a limit when you are antideriving, finding an arc length, or finding volume after rotating a function?