system
Given the following post, respond as if you're commenting on Reddit:
human
Eli5: Why do we study Limits in Calculus?
gpt
Calculus, both integral and differential calculus, is based upon limits.  We don't actually reach our answers but we get infinitely close to it.  You can't calculate instantaneous rate of change (the value of the derivative) without using two infinitely close points.  Well, you *do*, but not without using limits to derive that ability. The rules of differentiation can be derived (no pun intended) by taking the limit as delta approaches zero blahblahblah you know the rest.  Similarly, when calculating area, you're actually calculating the sum of an infinite number of rectangles.  As you approach an infinite number of rectangles, you approach the actual area under a curve.