TEST
До 10-летия сайта осталось:
` f(x)=sum_(n=0)^oo(f^((n))(a))/(n!)(x-a)^n `
` x_{1,2} = -b \pm \sqrt{b^2-4ac} / {2a} `
` f(a) = \frac{1}{2\pi i} \oint \frac {f(z)}{z-a}dz `
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[[a , b ],[c, d]]((n),(k))
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(a,b]={x in RR | a < x <= b}
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x/x={(1,if x!=0),(text{undefined},if x=0):}
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(df(x))/dx=lim_(h->0)(f(x+h)-f(x))/h
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f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz
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\cos(α+β)=\cosα·\cosβ−\sinα·\sinβ
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\int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot ndS
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\vec{\nabla} \times \vec{F} = ( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} ) \mathbf{i} + ( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} ) \mathbf{j} + ( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} ) \mathbf{k}
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\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}
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(\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i ( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m )
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{::}_(\ 92)^238U
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stackrel"def"= or \stackrel{\Delta}{=}" "("or ":=)
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`hat(ab) ` `bar(xy) ` `ulA ` `vec v ` `dotx ` `ddot y `
`\[\begin{matrix} \dot{x} & = & \sigma(y-x) \\ \dot{y} & = & \rho x - y - xz \\ \dot{z} & = & -\beta z + xy \end{matrix} \] `
`\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left(\sum_{k=1}^n a_k^2 \right) \left(\sum_{k=1}^n b_k^2 \right) \] `
`\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \] `
`\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \] `
`\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \] `
[ `e·sqrt{201}-sqrt{sqrt{9}} `]