The Shell Method is a technique for finding the volume of a solid of revolution. Just as in the Disk/Washer Method (see AP Calculus Review: Disk and Washer Methods), the exact answer results from a certain integral. In this article, we’ll review the shell method and show how it solves volume problems on the AP […]
As you prepare for the AP Calculus exam, it’s important to know what you’re getting into. Hopefully you’ve already taken a look at the list of topics, but this article is about one topic in particular: limits. Read on to familiarize yourself with the common limits that you’ll encounter on the test!
So you may have memorized all of the derivative rules. You might be able to derive f '(x) from f(x) no matter how complicated the function is. But how are you at estimating derivatives directly from the graph? As we’ll see in this review article, it’s all about slope! The Derivative Measures Slope Let’s begin with […]
Calculus is the study of motion and rates of change. In fact, Isaac Newton develop Calculus (yes, like all of it) just to help him work out the precise effects of gravity on the motion of the planets! In this short review article, we’ll talk about the concept of average rate of change. We’ll also […]
What’s a discontinuity? Any point at which a function fails to be continuous is called a discontinuity. In fact, there are various types of discontinuities, which we hope to explain in this review article. Points of Discontinuity The definition of discontinuity is very simple. A function is discontinuous at a point x = a if […]
You know you’ll have to know your derivatives inside and out in order to score high on the AP Calculus exam. But what are the most common derivatives you’ll see on the test? In this short article, we’ll let you in on the secret! Know the Basics First of all, it’s very important to have […]
The disk and washer methods are useful for finding volumes of solids of revolution. In this article, we’ll review the methods and work out a number of example problems. By the end, you’ll be prepared for any disk and washer methods problems you encounter on the AP Calculus AB/BC exam! Solids of Revolution The disk […]
The Ratio and Root Tests are indispensable tools for finding out whether a series converges or diverges. These tests also play a large role in determining the radius and interval of convergence for a series of functions. In this article, we will discuss how the Ratio and Root Tests work. In addition, you’ll see a […]
What is a geometric series? A series is the sum of the terms of a sequence. What makes the series geometric is that each term is a power of a constant base. For example, Each term in this series is a power of 1/2. Equivalently, each term is half of its predecessor. Whenever there is […]
This article reviews definitions and techniques for finding radius and interval of convergence of power series.