Oi vey, that does sound like an awful class. I've never had a really bad class... except Senior Seminar my last semester. The teacher was a biochemist, which is essentially the complete opposite of a physical chemist (which I consider myself). It was torture having to read biochemistry articles.
And that's actually a decent by-the-book definition of a limit! Essentially, if you have a function, say [f(x) = 1/x], x obviously can not be 0, by basic rules of mathematics. But what if it *could* be zero? That's a limit. Basically just approximation, say, taking x closer and closer to zero (such as, x = 0.000001, 0.00000001, and so on), and you get an converging value. Limits are so important because they're truly the foundation of calculus.
Derivatives are simply finding the slope of a single point of a curve (this is done by taking the slope of two points, the difference being "delta x", or dx, and the difference for y being dy, and you take the limit as dx --> 0, recalling that the equation of the slope, in this case, is the ever-famous dy/dx). Integration is finding the area under a curve, and this is done by making boxes within the curve with a width dx, summing them all up and taking the limit as dx --> 0). Those two things are the woodworking of calculus, but observe that they're both limits! And, as I always say, since limits are theoretical "what if's", then all of calculus is really in theory (because recall, for example, the slope being [lim @ dx-->0 (dy/dx)], dx can't "really" be 0), and that's what's so interesting about calculus, in my opinion!
I've spent so much time in a lab-oriented atmosphere that I virtually forget what it's like to be in a traditional class. I kind of miss it; luckily, my teacher for Inorganic Chem taught in a very traditional, lecturing way. It was very refreshing, since most of my department taught by a method pioneered by our Organic teacher called "POGIL").