LaTex数学符号+代码运行结果

\[ \Gamma_{ij}^{k} =\frac{1}{2}(\frac{\partial g_{il}}{\partial u^j} +\frac{\partial g_{jl}}{\partial u^i} -\frac{\partial g_{ij}}{\partial u^l}) \] \[\sum_{i,j,k=1}^{\infty}{x_{i_{j_{k}}}}\] \[\frac{f(x)}{g(x)}\] \[\frac{x}{y}+\frac{f(x)}{g(x)}\] \[\lim_{x\rightarrow x^0}f(x)=A\] \[\lim_{x\rightarrow x_0}f(x)=A\] $\int^a_dc_b f(x)dx$\(\int^a_dc_b f(x)dx\) \[\int^a_dc_b f(x)dx\] \[\sum_{i=1}^{\infty} x_i\] \[\sqrt[5]{x^4-3x+1}\] Errors=\(\sqrt{\frac{\sum_{j=1}^{M}[predictior(j)-real(j)]^2}{M}}\) \[\iint_{\Omega}f(x,y)dxdy\] \[\iiint_{\Gamma}f(x,y,z)dxdydz\] \[ \left|\begin{array}{cccc} 1 & 6 & 9 \\ 7 & 90 & f(x)\\ 9 & \psi(x) & g(x) \end{array}\right| \] \[ \left[\begin{array}{cccc} 1 & 6 & 9 \\ 7 & 90 & f(x)\\ 9 & \psi(x) & g(x) \end{array}\right] \] \[ \left(\begin{array}{cccc} 1 & 6 & 9 \\ 7 & 90 & f(x)\\ 9 & \psi(x) & g(x) \end{array}\right) \] \[ \left(\begin{array}{llll} 1 & 6 & 9 \\ 7 & 90 & f(x)\\ 9 & \psi(x) & g(x) \end{array}\right) \] \[ \left(\begin{array}{rrrrr} 1 & 6 & 9 \\ 7 & 90 & f(x)\\ 9 & \psi(x) & g(x) \end{array}\right) \] \[ \begin{cases} \ u_{tt}(x,t)= b(t)\triangle u(x,t-4)&\\ \ \hspace{42pt}- q(x,t)f[u(x,t-3)]+te^{-t}\sin^2 x, & t \neq t_k; \\ \ u(x,t_k^+) - u(x,t_k^-) = c_k u(x,t_k), & k=1,2,3\ldots ;\\ \ u_{t}(x,t_k^+) - u_{t}(x,t_k^-) =c_k u_{t}(x,t_k), &k=1,2,3\ldots\ . \end{cases} \] \[ q(x,t)= \begin{cases}(t-k+1)x^2,\quad \ \ & t\in\big(k-1,k-\dfrac{1}{2}\big],\\ (k-t)x^2, \quad \ \ & t\in\big(k-\dfrac{1}{2},k\big], \end{cases} \]

代码运行结果：