What's a Limit?

Once we delve into calculus, understanding the notion of a limit will be critical.  In case you've never discussed limits before, first consider the everyday meaning of the word.  The Speed Limit is a decent analogy to a mathematical limit, in that you can legally drive at a speed up to or including the actual limit. You don't have to drive the actual speed limit. The key is in not exceeding it.  In calculus, you'll be finding the "speed limit" and the function is like the car.  Whether or not the function actually reaches the limit is not important.  The limit will be the y-value that the function targets.   


Here's an example.  I'll have to give you a location on the function (an x-value) for you to mentally zoom in on.  Consider the function y = x.  Picture the graph and focus on the piece near the origin.

As x approaches 0, either from the left or from the right, what y-value is the graph moving toward?


You should be getting 0 and, in this case, the function actually reaches its limit.

For your post, I'd like you to consider any function that you know.  Everyone's function should be different.  State the function (use ^ for exponents), tell me where to zoom in on the x's, and give the y-value that the function approaches.

Welcome, AP students! I'm so glad that you're here. The study of calculus is amazing in its "complicated simplicity" and I'm excited to watch you learn it. Newton and Leibniz (the fathers of calculus) were brilliant indeed but their discoveries were inevitable. The Creator of our universe is the Creator of math - no doubt in my mind. I firmly believe that most of math is discovered ~ not invented ~ and I hope that I can convince you of that (if you're not already there).

For your first post, I'd like you to take a few minutes to think about topics in high school math that you have found difficult. If you've done a complete brain-dump since May, google 'pre-calculus topics' or something similar and look through the contents. Even if you eventually nailed a topic, let me know if it was tough for you at first. This will help me to target specific holes that you all might have.

Again, welcome aboard. Take this class seriously - I promise you that I will! Have a great weekend.