Sample Latex

^nC_r = \frac{n!}{(n-r)! r! } \frac{1}{2} \sqrt{1} \frac{n(E)}{n(S)} \frac{1}{n}

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\frac{\frac{150}{100} x }{  \frac{90}{100} y} \frac{1}{2}Calculate (144^{-312}) ?144^(-312)^1/6 \frac{1}{2} \

 \frac{(1+2)}{(2 +\frac{4}{3})}\\

x^2 \frac{1}{2} \

 \frac{(1+2)}{(2 +\frac{4}{3})}\\

\frac{1}{7}=0.\overline{142857} (\frac{1}{2})^2 \ \implies \neq \ a_1 + a_5 \ \overline{A} c^2018*\tfrac{\pi }{180^{\circ}}\frac{Pl}{2}\frac{\alpha ^{n}+\beta ^{n}}{\frac{1}{\alpha ^{n}}+\frac{1}{\beta ^{n}}}

n * βn)

t\frac{\partial x}{\partial t} + x = t \text{ is }IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = tx^{x} = (e^{i\tfrac{\pi }{2}})^{x}A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )\frac{1}{2\pi j}\oint_{C} f(z)dz\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0\iint_{s} 5\vec{r}\cdot \hat{n}dS \text{ is}

To write Augmented matrix:

{\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}\begin{vmatrix}1&  1& 1& :& 6\\1& 4&  6& :& 20\\1& 4& \lambda &  :& \mu \\\end{vmatrix}=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )=\left [ x^{4}+32x^{5} \right ]^{1}_{0}=33\iiint \bigtriangledown\cdot  Pdv

     

A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0

A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha

A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha

15\frac{1}{2}{12}^C_{3} = 220\frac{2}{4}\begin{bmatrix}2 &4\\ 2 & 5\end{bmatrix}

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_{}
\frac{1}{2}
\frac{1}{\sqrt{3}}
\sqrt{3}
x^{\frac{1}{a}}
 
\frac{P × R × T}{100}
 
\mathbf{\frac{P × R × T}{100}}
 
[latex]P (1+ \mathbf{\frac{r}{100}})^{n}[/latex]
 
 P (1+ \frac{r}{100})^{n}
 
(\frac{A}{P})^{\frac{1}{t}}
 
 
\mathbf{ P (1+ \frac{{\frac{r}{2}}}{100})^{2n}}
 
(1+ \mathbf{\frac{\frac{3}{2}r}{100}})
 
\frac{r_{1}}{100}
 
\frac{P × (R)^2}{(100)^2} × \frac{(300 + R) }{100}
 
\frac{P × (R)^2}{(100)^2}
 
==========linear equation ===========
\frac{}{}
– \frac{b}{a}
p_{1}x +q_{1}y = r_{1}
=============quadratic equation =================
\frac{-b  \pm  \sqrt{b^2 – 4ac}}{2a}
=====coordinate geometry======
\sqrt{(x_{2}- x_{1})^2 + (y_{2}- y_{1})^2}
\sqrt{2}\frac{(y_{1}- y_{2})}{(x_{1}- x_{2}}\frac{ m x_{2} + nx_{1}}{m + n}\frac{my_{2} + ny_{1} }{m + n}\frac{x_{1}+ x_{2} + x_{3}}{3}\frac{y_{1}+ y_{2} + y_{3}}{3}\frac{1}{2} × (x_{1}(y_{2}-y_{3}) + (x_{2}(y_{3}-y_{1})  ) + (x_{3}(y_{1}-y_{2})  )