Category: math

The Art of Studying Smart

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Most of the world tends to look down upon the idea of procrastination with a frown. She’s lazy. She’s not responsible. She doesn’t have a work ethic. My view of this concept is slightly different. I wish I could slip back into my elementary school days as a model student, but I’m barely learning yesterday’s content by the time tomorrow rolls around. My stress levels and recent academic performance, on the other hand, tell an entirely different story. Procrastination might not be for everyone—some people need rigid schedules for their personal sanity and success, and these individuals should be held in high regard. For the rest of us: if we learn how to properly procrastinate, we could have all the success and time in the world. In fact, there are three simple steps to embracing the art: always keeping the task in the back of your head, being able to self-discipline when it’s time to work, and knowing your personal capabilities and limits. 

Calculus: Infinite Limits vs Limits at Infinity with Explanations, Practice Questions, and Answers [AP Calculus, Calculus 101, Math]

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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.

Calculus: Limits vs Continuity with Explanations, Practice Questions, and Answers [AP Calculus, Calculus 101, Math]

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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!

Calculus: Limits with Explanations, Practice Questions, and Answers [AP Calculus, Calculus 101, Math]

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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.

Calculus: Two Important Theorems – The Squeeze Theorem and Intermediate Value Theorem

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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.

The Rise of Tech: Tech Trends of the COVID-19 Pandemic

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The recent COVID-19 pandemic has turned our world upside down. From the way we greet each other to the schedule of our daily routines, it’s safe to say that everything that was considered the norm at the beginning of 2020 has completely changed. While most people’s eyes are on health officials, tech giants and start-up companies have been using this time to create new inventions to propel society further – or so they say. Here we will analyze the new products and tech trends that have arisen in the wake of this pandemic, what they do, and if they actually serve to help society.

Soft Robotics 101: Definition, Examples, and Soft Robotics Applications

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When you hear the word “robot”, what image usually comes to mind? Is it a metallic, boxy machine? A sleek android that talks to people? A robot is a machine that is automatically operated and completes tasks in replacement for humans. Some robots are humanoid and have actions that resemble human movement, such as ASIMO (Advanced Step in Innovative Mobility), a robot created by Honda that can walk with two legs (Honda).

AP Calculus: Limits and Continuity

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A lesson plan look at the relationship between limits and the continuity of a function for calculus. In the last article, we started talking about limits and their applications for analyzing functions. In this article, we will look at how limits can be used to determine the continuity of a function at a point.