📘 mathematics

1. The user asks for all formulas used in math. 2. There are many formulas across different branches of math such as algebra, geometry, calculus, and physics.

1. Тодорхойлолт: f(x) функц нь (0; \pi) завсарт өгөгдсөн байна. \n\n2. Зорилго: f(x)-г тэгш болон сондгой функц байхаар үргэлжлүүлж, Фурьегийн цуваанд задлах.\n\n3. Фурьегийн цувра

1. Дано множество A = \{1, 2, 3, 4, 5\} и множество B = \{4, 5, 6, 7\}. Найдите \(A \cup B\) (объединение множеств). 2. Для тех же множеств A и B найдите \(A \cap B\) (пересечение

1. **حل المعادلة 8x^3 - 27 = 0** - المعادلة من الشكل $$a^3 - b^3 = 0$$ حيث $$a = 2x$$ و $$b = 3$$.

1. Problem: Find $n(B)$ if $n(A \times B) = 6$ and $A = \{1, 3\}$. Formula: $n(A \times B) = n(A) \times n(B)$.

1. **Problem Statement:** Define the following terms with examples: (a) ε - δ definition of a limit of a function μ(x)

1. Let's start by understanding what it means to apply a formula in math appropriately. 2. A formula is a mathematical rule or relationship expressed using symbols and variables.

1. **Énoncé du problème :** Déterminer la valeur de vérité et la négation des propositions données.

1. **Problem Statement:** Understand the mathematical constant $e$ and its value. 2. **Definition:** The number $e$ is a fundamental mathematical constant known as Euler's number.

1. **Problem Statement:** Calculate the factorial of a very large number, such as $1000!$. 2. **Definition:** The factorial of a positive integer $n$, denoted $n!$, is the product

1. The problem is to understand what "pure maths" refers to and its scope. 2. Pure mathematics is the branch of mathematics that deals with abstract concepts and theoretical framew

1. The problem is to understand the concept of consistency in a mathematical or logical context. 2. Consistency means that a set of statements or equations does not contain any con

1. The problem asks to identify the figure represented by the number $2 \times 10^{48}$. 2. This number is written in scientific notation, where $2$ is the coefficient and $10^{48}

1. The problem is to find the general solution of a differential equation or algebraic problem (please specify the exact problem for precise solution). 2. Generally, for a differen

1. **Problème 1 : Montrer que $\frac{(4^{n+1} + 4^n)^2}{(2^{2n+1} - 2^{2n})^2} \in \mathbb{N}$ pour $n \in \mathbb{N}$.** 2. **Comparer : $2 - \sqrt{5}$ et $\frac{-1}{2 + \sqrt{5}}

1. The problem is to understand the concept of "notation" in mathematics and how to use it effectively. 2. Notation is a system of symbols and signs used to represent numbers, oper

1. The problem is to understand and apply key concepts in functions, trigonometry, differential calculus, and hypothesis testing, including definitions, rules, and examples. 2. Let

1. **Problem 1: Find the mean, median, and mode of the numbers:** 17, 18, 16, 17, 17, 14, 22, 15, 16, 17, 14, 12. 2. **Mean formula:** $$\text{Mean} = \frac{\text{Sum of all number

1. Let's start by understanding the number 6. The number 6 is a natural number that comes after 5 and before 7. 2. In mathematics, 6 is considered a composite number because it has

1. State the problem. Problem: Create and solve several advanced percentage problems suitable for grade 7 and show full step-by-step solutions.

1. The user requests notes on a wide range of advanced math topics including number theory, algebra, functions, inequalities, geometry, sequences, probability, data analysis, and c