- #1

NoahsArk

Gold Member

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*My question now is should I even be getting hung up on it when I'm learning calculus*? If a student of calculus has a basic understanding of derivatives and integrals, and knows how to solve standard calculus problems, is it just a distraction to be thinking about things like this? I also don't understand the solution to Xeno's paradox, which seems like it also involves an understanding of limits, but that also seems like a distraction to be thinking about in learning calculus.

I've noticed in my studying of different subjects I often will go down a culdesac in trying to understand exactly how something works, and this comes at the expense of not learning the basic material of the subject. If for, example, I am able to solve basic calculus problems like finding derivatives, finding minimum and maximum points, and if I understand the general idea of what derivates are, does it matter that I don't understand exactly how limits give us the exact slope of a tangent line (or how they help give us the exact area under a curve as opposed to a super close approximation)? Calculus problems in school and online lessons do not ask the student about the nature of limits. They do ask students to find what the limit is of a certain function as x approaches a value, and those are easier for me to deal with than to think about how limits work on a deeper level.