📘 mathematics

1. The problem: Understand what a Fourier series is and how it represents periodic functions. 2. A Fourier series expresses a periodic function $f(x)$ as a sum of sines and cosines

1. **State the problem:** Calculate the percentage weight (grade) of 25 marks if the total marks are 25.

1. The problem is to understand the chapter "Mensuration" which deals with measuring the surface area and volume of different geometric shapes. 2. Mensuration formulas are used to

1. प्रश्न: निम्न के लिए भिन्न लिखिए - (i) तीन चौथाई भाग (अ) $\frac{5}{3}$ (ब) $\frac{4}{3}$ (स) $\frac{3}{7}$ (द) $\frac{3}{4}$ 2. प्रश्न: निम्न का अन्तर ज्ञात कीजिए - $\frac{13}{1

1. The problem is to understand how to represent numbers on a number line. 2. A number line is a straight line where each point corresponds to a real number.

1. The problem is to calculate $3 \times 10^{-3} \times 600$. 2. We use the rule of exponents and multiplication: multiply the numbers and powers separately.

1. **Problem:** Three metallic cubes with edges 3 cm, 4 cm, and 5 cm are melted to form a single cube. Find the edge length and surface area of the new cube. 2. **Formula:** Volume

1. You have shared your math syllabus which includes Coordinate Geometry, Surface Area and Volume, Functions, Quadratics (Standard Form, Vertex Form, Factorized Form), and Sequence

1. The problem is to understand and compare quantities, a key concept in Class 8 NCERT math. 2. Comparing quantities involves finding the ratio or difference between two or more qu

1. The problem is to verify whether a given function is a metric on $\mathbb{R}^n$. 2. A function $d: \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}$ is a metric if it satisfies t

1. **Problem:** Calculate the average of the numbers 4, 8, and 12. 2. **Formula:** The average (mean) of $n$ numbers $x_1, x_2, ..., x_n$ is given by:

1. **Problem Statement:** Define a convex function. 2. **Definition:** A function $f: \mathbb{R}^n \to \mathbb{R}$ is called convex if for all $x, y \in \mathbb{R}^n$ and for all $

1. Let's start by understanding what a function is. A function is a rule that assigns each input exactly one output. For example, if you have a function $f(x) = x^2$, it means for

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.