demo for latex

Welcome to your first post using KaTeX! Below are examples of inline and block LaTeX equations, images, and a YouTube video.

🧠 Inline LaTeX Examples:

Let's define a function: \( f(x) = 3x^2 + 2x - 5 \)

The derivative of this function is: \( f'(x) = 6x + 2 \)

📐 Block LaTeX Equation:

\[ \int_{0}^{1} x^2 \, dx = \left[ \frac{x^3}{3} \right]_0^1 = \frac{1}{3} \]

📊 Limit and Derivative Definition:

\[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]

🧮 Trigonometric Identity:

\[ \sin^2 \theta + \cos^2 \theta = 1 \]

📷 Image Example (with zoom effect):

🎥 YouTube Video Example:

✅ Conclusion

This post includes:

• Inline math using \( \text{\\(...\\)} \)
• Block equations using \[ \text{...} \]
• KaTeX rendering
• Image with zoom effect
• YouTube video lazy-loaded

Happy blogging! 😊