LaTex 测试

众所皆知，LaTex 是个好东西，本站自然也引进了它。

下面来个小小的测试。

$$\frac{2333}{6666}$$

$$f(x_1,x_x,\ldots,x_n) = x_1^2 + x_2^2 + \cdots + x_n^2 $$

$$\sum_{i=1}^n a_i=0$$

$$f(x)=x^{x^x}$$

$$[f(x,y,z) = 3y^2 z \left( 3 + \frac{7x+5}{1 + y^2} \right).]$$

$$\frac{du}{dt} and \frac{d^2 u}{dx^2}$$

$$\frac{\partial u}{\partial t}= h^2 \left( \frac{\partial^2 u}{\partial x^2}+ \frac{\partial^2 u}{\partial y^2}+ \frac{\partial^2 u}{\partial z^2}\right)]$$

$$[ \lim_{x \to 0} \frac{3x^2 +7x^3}{x^2 +5x^4} = 3.]$$

$$[ \int_{x^2 + y^2 \leq R^2} f(x,y)\,dx\,dy= \int_{\theta=0}^{2\pi} \int_{r=0}^Rf(r\cos\theta,r\sin\theta) r\,dr\,d\theta.]$$

$$[ \int_0^R \frac{2x\,dx}{1+x^2} = \log(1+R^2).]$$

$$[ \int !!! \int !!! \int_V
\left| \psi(\mathbf{r},t) \right|^2\,dx\,dy\,dz]$$