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Limit of a function: Introduction – Calculus

In order to study a function and its behavior and properties, an important step is to find out the limits of the function on the ends of its domain of definition. In this article, we will introduce the idea of limits and the different cases that we can come across. Table of content: Introduction...

Mathematical functions: Definition and Properties

While studying mathematics you may have noticed that functions are widely used in nearly every subject. In a matter of fact, they are one of the most basic and fundamental objects in mathematics, so in this article, we will learn about functions, their definition, and their properties. Table of...

How to solve equations of 1st, 2nd and 3rd degree

We may face the task of solving different types of equations while studying mathematics, so in this post, we will see how to solve first, second, and third degree equations. Table of content: Possible cases for the solutions Solving first degree equations Solving second degree equations Solving...

Absolute Value and Square Roots

Absolute values often show up in problems involving square roots. That’s because you can’t take the square root of a negative number without introducing imaginary numbers (those involving $i = \sqrt{-1}$ ). Example 1: Simplify $\sqrt{x^{2}}$ This problem looks deceptively simple. Many students...

Absolute Value and Logarithms

Absolute Value and Logarithms Absolute values often turn up unexpectedly in problems involving logarithms. That’s because you can’t take the log of a negative number. Let’s first review the definition of the logarithm function: Logb x = y ⇔ by = x (The double arrow is a bi-conditional, which means...

L’Hospital’s Rule

L’Hospital’s Rule is a useful way to evaluate tricky limits. It is most often used for limits of indeterminate form. The rule is as follows: If $f(x)$ and $g(x)$ are differentiable on some interval around the number $a$ (or if $a=\infty$, $f(x)$ and $g(x)$ are differentiable for all...

Algebraic Groups

Introduction to Algebraic Groups One of the most fundamental algebraic structures in mathematics is the group. A group is a set of elements paired with an operation that satisfies the following four conditions: I. It is closed under an operation (represented here by “+”, although it does not...