KaTeX is a powerful tool for typesetting mathematical expressions on the web, and it's especially useful for those who use Markdown for their documentation needs. Markdown is a lightweight markup language that allows you to write formatted text using a simple syntax. With KaTeX, you can now include complex mathematical equations in your Markdown files with ease.

Here are four examples of how to use KaTeX in Markdown:

The quadratic formula is given by

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

where a, b, and c are constants.

```
The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $c$ are constants.
```

In this example, we're using KaTeX to typeset a fraction within a Markdown paragraph. The equation is enclosed in double dollar signs, which tells KaTeX to render it as a block element.

The sum of the first n positive integers is given by:

\sum_{i=1}^{n} i = \frac{n(n+1)}{2}

```
$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$
```

In this example, we're using KaTeX to typeset a summation equation with a limit and a fraction within a Markdown blockquote. The equation is enclosed in double dollar signs, which tells KaTeX to render it as a block element.

Here's an example of a 3x3 matrix:

\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}

```
$$
\begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{pmatrix}
$$
```

In this example, we're using KaTeX to typeset a matrix within a Markdown code block. The matrix is enclosed in double dollar signs, which tells KaTeX to render it as a block element.

The limit of the function

f(x) = \frac{\sin x}{x}

as x approaches 0 is:

\lim_{x \to 0} f(x) = 1

```
The limit of the function $$f(x) = \frac{\sin x}{x}$$ as $x$ approaches $0$ is:
$$\lim_{x \to 0} f(x) = 1$$
```

In this example, we're using KaTeX to typeset a limit equation within a Markdown paragraph and a fraction within a Markdown inline code block. The equation is enclosed in double dollar signs, which tells KaTeX to render it as a block element.

These are just a few examples of what you can do with KaTeX in Markdown. The library supports a wide range of mathematical symbols and functions, including integrals, limits, derivatives, and more. You can find a full list of supported symbols and functions in the KaTeX documentation.

In conclusion, KaTeX is a powerful tool for typesetting mathematical expressions in Markdown files. With its fast and lightweight design, it's a great choice for anyone looking to include math in their documentation. So why not give it a try and take your math to the next level?