Introduction Everyone knows \(\pi\). The ratio between the circumference and diameter of a circle is often approximated as 3.14. For many, it’s the first irrational number they encounter—a number so renowned that it even has its own day of celebration. But how was \(\pi\) actually discovered? The history of \(\pi\) stretches over thousands of years,…
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Have you ever had trouble remembering when sines, cosines, and tangents are positive or negative? If so, you may want to remember the mnemonic ASTC, which stands for All, Sine, Tangent, Cosine and can be remembered as “All Students Take Calculus.” The acronym tells you which trig functions are positive in each quadrant, starting from…
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The derivative is a calculus superpower that gives great insights into functions. The first and second derivatives allow us to find the function’s local minima and maxima, known as critical points, as well as the function’s inflection points. This article will show you exactly how to use derivatives to find critical points and the importance…
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Derivatives are one of the most important concepts in calculus. They describe the rate of change of a function with respect to a variable. However, not every function has a derivative. In this article, we will explain how to determine whether or not a given function has a derivative, as well as how to determine…
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Calculus is one of, if not the most, important branches of mathematics. There are many important calculus terms that all calculus students need to know. This guide will introduce and explain 8 important terms that are the cornerstones of calculus. Some of these are formulas, while others are concepts and definitions. Introduction to Calculus Terms…
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Calculus is a superpower in math. From predicting planetary orbits to optimizing internet speeds, it’s been a cornerstone of countless advancements. But who invented this power tool? Actually, it took the collective genius of many mathematicians over millennia to develop the calculus we know today. Ancient Calculus Eudoxus and the Method of Exhaustion Imagine trying…
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The first fundamental theorem of calculus links differentiation and integration, two core concepts of calculus. In this article, we will explore the intricacies of the first fundamental theorem of calculus, breaking down its components, implications, and applications. It is possible that your teacher or textbook call this theorem “The second fundamental theorem of calculus”, as…
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The second fundamental theorem of calculus, sometimes called the second FTC, is a formula that allows for the evaluation of definite integrals. In this article, we will explore what the second half of the fundamental theorem of calculus states, how it functions in practice, and how it is connected to the first fundamental theorem of…
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Calculus is a branch of mathematics that studies and deals with change, as well as the rate and accumulation of said change. Calculus has applications throughout the scientific world, but it also plays a large role in business. One of the most important parts of operating a successful business is being able to react to…
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The AP Calculus BC Exam is a rigorous test that requires good preparation. The best way to study for it is to complete and score practice exams in order to track your progress throughout your studies. This blog post will act as your own personal AP Calculus BC score calculator and will help you on…
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