$$\documentclass{article} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amssymb} \title{LaTeX Formula Samples} \author{Gemini} \date{April 2026} \begin{document} \maketitle \section{Physics} The relation between energy and mass is given by the famous equation: \begin{equation} E = mc^2 \end{equation} Newton's Law of Universal Gravitation: \[ F = G \frac{m_1 m_2}{r^2} \] \section{Calculus} The Fundamental Theorem of Calculus: \[ \int_{a}^{b} f(x) \, dx = F(b) - F(a) \] Euler's Identity: \[ e^{i\pi} + 1 = 0 \] \section{Linear Algebra} The identity matrix $I$ is defined as: \[ I = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \] The determinant of a $2 \times 2$ matrix: \[ |A| = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc \] \section{Statistics} The probability density function for the normal distribution: \[ f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2} \] \section{Chemistry} The chemical equation for photosynthesis: \[ 6CO_2 + 6H_2O \rightarrow C_6H_{12}O_6 + 6O_2 \] \end{document}$$Standard Table

Product	Category	Price
Apple	Fruit	$1.00
Bread	Bakery	$2.50
Milk	Dairy	$3.99

Table with Alignment

Left Aligned	Center Aligned	Right Aligned
Text goes left	This is centered	Text goes right
Column 1	Column 2	Column 3
$10.00	$500.00	$1,000.00

Large Comparison Table

Feature	Basic Plan	Pro Plan	Enterprise
Storage	10GB	100GB	Unlimited
Users	1 User	5 Users	Unlimited
Support	Email	24/7 Chat	Phone + Chat
Price	Free	$12/mo	Contact Us

Mathematical Notation (LaTeX)

1. Inline Formulas
The Pythagorean theorem is $a^2 + b^2 = c^2$.
The limit definition of a derivative is $f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$.

2. Display Blocks (Centered)

Quadratic Formula:
$$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Summation (Sigma):
$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$

Integration:
$$\int_{a}^{b} x^2 , dx = \left[ \frac{x^3}{3} \right]_a^b$$

Matrix:
$$
\begin{matrix}
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1
\end{matrix}
$$

Greek Letters & Symbols:
$$\alpha, \beta, \gamma, \Delta, \theta, \infty, \pi$$

hr;;

Mathematical Notation (LaTeX)

1. Inline Formulas
The Pythagorean theorem is $a^2 + b^2 = c^2$.
The limit definition of a derivative is $f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$.

2. Display Blocks (Centered)

Quadratic Formula:
$$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Summation (Sigma):
$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$

Integration:
$$\int_{a}^{b} x^2 , dx = \left[ \frac{x^3}{3} \right]_a^b$$

Matrix:
$$
\begin{matrix}
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1
\end{matrix}
$$

Greek Letters & Symbols:
$$\alpha, \beta, \gamma, \Delta, \theta, \infty, \pi$$

Standard Table

ProductCategoryPriceAppleFruit$1.00BreadBakery$2.50MilkDairy$3.99

Table with Alignment

Left AlignedCenter AlignedRight AlignedText goes leftThis is centeredText goes rightColumn 1Column 2Column 3$10.00$500.00$1,000.00

Large Comparison Table

FeatureBasic PlanPro PlanEnterpriseStorage10GB100GBUnlimitedUsers1 User5 UsersUnlimitedSupportEmail24/7 ChatPhone + ChatPriceFree$12/moContact Us

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Heading 2

Heading 3

Bold Text
Italic Text
Bold and Italic
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Lists

Unordered List:

Item A
Item B
- Sub-item B1
- Sub-item B2

Ordered List:

First step
Second step
Third step

Task List:

Finished task
Pending task

Blockquotes

This is a blockquote. It’s often used to highlight quotes or external references.
This is a nested blockquote.

Code

Inline Code: const greeting = "Hello World";

Code Block (Javascript):

function welcome() {
  console.log("Markdown is awesome!");
}

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