I'm still very new to the world of calculus and physics, and while I understand how to do limits and such, I don't understand the usefulness of them, and I'm hoping some of you can help me understand why limits are important and why we bother with them. Here's my understanding of them currently: to find when a function either has an upper bound (or lower bound) at a certain value or beyond. My question is (and probably due to inexperience) is, when writing functions, wouldn't you already know where the limits would be? I mean, you wouldn't throw in arbitrary values into a function that you're applying to a system, so wouldn't you already know where the function will end (or I guess in some cases, break)? Is there an example of where, or why, limits are useful?