如 $\lim_{x \to 0} \frac{\sin x}{x}$ 渲染的是

$$
\begin{eqnarray}
\lim_{x \to 0} \frac{\sin x + x^2 + x^3}{x} & = & \lim_{x \to 0} \frac{\sin x }{x} + \lim_{x \to 0} \frac{x^2 }{x} + \lim_{x \to 0}\frac{x^3}{x}
\\ & = & \lim_{x \to 0}\frac{\sin x}{x}
\\ & = & 1
\end{eqnarray}
$$

斐波那契数列$A_n=A_{n-1}+A_{n-2}$,前后两项的比值逐渐收敛到黄金分割比例
$$\lim_{n\to \infty}\frac{A_{n-1}}{A_n}=\frac{\sqrt{5}-1}{2}.$$

因式分解
$$\begin{split}(x−1)(x−3)&=x^2−4x+3 \
&=x^2−4x+4−1 \
&=(x−2)^2−1
\end{split}
$$

狄利克雷函数

$$
D(x)=
\begin{cases}
1,& x \in Q \
0,& x \notin Q
\end{cases}
$$

高斯公式
$$
\iiint_{\Omega}\left(\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}+\frac{\partial R}{\partial z}\right) d v=\iint_{\Sigma} P d y d z+Q d z d x+R d x d y
$$

物理公式

• 牛顿第一定律: $\sum \vec{F}_{i}=\frac{\mathrm{d} \vec{v}}{\mathrm{d} t}=0$
• 牛顿第二定律: $\vec{F}=\frac{\mathrm{d} m}{\mathrm{d} t} \vec{v}+m \frac{\mathrm{d} \vec{v}}{\mathrm{d} t}=\frac{\mathrm{d} m}{\mathrm{d} t} \vec{v}+m \vec{a}=\frac{\mathrm{d} m}{\mathrm{d} t} \vec{v}+m \frac{\mathrm{d}^{2} \vec{r}}{\mathrm{d} t^{2}}$
• 牛顿第三定律: $\overrightarrow{F_{12}}=-\overrightarrow{F_{21}}$
• 质能守恒: $E=mc^2$

化学公式

离子反应与沉淀: $\ce{SO4^2- + Ba^2+ -> BaSO4 v}$

生物公式

光合作用
范德蒙行列式
$$D_{n-1}=\left|\begin{array}{cccc}
1 & 1 & \dots & 1 \
x_{2} & x_{3} & \dots & x_{n} \
\vdots & \vdots & & \vdots \
x_{2}^{n-2} & x_{3}^{n-2} & \dots & x_{n}^{n-2}
\end{array}\right|=\prod_{2 \leq j<i \leq n}\left(x_{i}-x_{j}\right)$$

Welcome to Hexo! This is your very first post. Check documentation for more info. If you get any problems when using Hexo, you can find the answer in troubleshooting or you can ask me on GitHub.

Quick Start

Create a new post

1

$ hexo new "My New Post"

More info: Writing

Run server

1

$ hexo server

More info: Server

Generate static files

1

$ hexo generate

More info: Generating

Deploy to remote sites

1

$ hexo deploy

More info: Deployment

这是一个中文测试