Happy New Year! We have all wanted something in our lifetime, and we have all probably experienced both the bitter taste of rejection and the sweet taste of getting what we want. Although many might believe that getting what you want is dependent on luck, there are certain things that separate high achievers. If you are to get what we want, you should set goals, and use strategies that allow you not only to influence people so you achieve what you want, but also get you closer to your wildest dreams.
In this article, Infinite limits are limits that evaluate to infinity. You can, however, have limits that are evaluated at infinity or have an evaluated value of infinity. While infinity is a strange concept, we can use it to determine the behavior of functions. This leads us to the discussion of infinite limits and limits at infinity.
In the last two articles, we talked about limits and their application in determining the continuity of a function. Here, we will apply those skills to few practice questions. Attempt the problems on your own at first; however, if you get stuck, the solution to each problem is just below it. These problems vaguely range from easy to hard. Enjoy!
In this chapter, we will introduce the first big idea in AP Calculus: Limits and Continuity. This a topic that is included in both the AB and BC Calculus courses. Even if your course hasn’t started yet, a good way to prepare yourself for it is to study limits, as they are generally easy to grasp. This will give you a head start on (most likely) the first topic you will learn in your AP calculus course, and can inhibit you from falling behind.
In this calculus article, we will talk about the methods for actually solving or evaluating limits. There are practice questions included, labeled PRACTICE, and they are there for you to test your understanding of the different methods. The answers are at the very bottom. Enjoy!
Learn about two very cool theorems in calculus using limits and graphing! The squeeze theorem is a useful tool for analyzing the limit of a function at a certain point, often when other methods (such as factoring or multiplying by the conjugate) do not work. This theorem also has other names like the Sandwich Theorem or the Pinch Theorem, but it is most commonly called the Squeeze Theorem. The Intermediate Value Theorem, often abbreviated as IVT, deals with a single function unlike the Squeeze Theorem.