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\[k_{i}= \frac{x_{i}}{ \sum x_{i}}\] |
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\[X_{t_{2}}-X_{t_{1}}, \ldots,X_{t_{n}}-X_{t_{n-1}}\] |
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\[\sum_{i=1}^{n+1}i= \sum_{i=1}^{n}i+(n+1)= \frac{n(n+1)}{2}+n+1\] |
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\[\lim_{y \rightarrow xf(y)=f(x)}\] |
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\[b^{3}-3/2b\] |
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\[1 \pm \sqrt{2}\] |
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\[\frac{n+1-1}{n+1}= \frac{n}{n+1}\] |
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\[\frac{ \sqrt{6}+ \sqrt{2}}{4}\] |
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\[(y^{ \frac{1}{b}})^{b} \leq(x^{ \frac{1}{b}})^{b}\] |
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\[\frac{3x}{3}+ \frac{1}{3}= \frac{4}{3}\] |
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\[-39\] |
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\[milli\] |
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\[\theta+e \alpha\] |
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\[\Delta^{kx}\] |
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\[F(b)-F(a)\] |
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\[\frac{az^{-1}(1+az^{-1})}{(1-az^{-1})3}\] |
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\[\sum_{i=1}^{n}a^{2}=a^{2} \sum_{i=1}^{n}1=na^{2}\] |
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\[\sin x-x \cos x\] |
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\[1,000_{,}000_{,}000\] |
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\[c_{x}c_{x+1}\] |
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\[G \times H\] |
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\[\sum_{k=1}^{n}a_{k}= \sum_{i=1}^{n}a= \sum_{j=1}^{n}a_{j}\] |
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\[a^{n}+( \frac{1}{a})^{n}\] |
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\[r \geq 1\] |
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\[\mu \geq 0\] |
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\[\frac{3 \times 3^{2}}{2}+ \frac{5 \times(-5)^{2}}{2}= \frac{3 \times v_{1}^{2}}{2}+ \frac{5 \times v_{2}^{2}}{2}\] |
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\[Y_{t+1}\] |
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\[\sqrt{4x^{5}+x}\] |
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\[17\] |
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\[1-2a+b-2ab=1-2b+a-2ab\] |
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\[x^{i}e_{i}= \sum_{i}x^{i}e_{i}\] |
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\[\frac{319}{28}=11.39\] |
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\[- \frac{11 \pi}{8}\] |
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\[[ \frac{1}{2} \sin^{2}(1)]-[ \frac{1}{2} \sin^{2}(0)]\] |
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\[\alpha^{2}+ \beta^{2}=( \alpha+ \beta)^{2}-2 \alpha \beta\] |
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\[0+A\] |
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\[f^{(i+k)}(0)=f^{(i)}(0)f^{(k)}(0)\] |
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\[S/V\] |
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\[\frac{n_{A}}{n}\] |
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\[f(x)= \frac{ \infty}{ \infty}\] |
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\[[B]\] |
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\[60^{o}\] |
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\[n \geq 0\] |
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\[\lim \frac{|a_{n+1}x|}{|a_{n}|}<1\] |
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\[\log a+ \log b= \log ab\] |
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\[\sum_{k=1}^{n}(ca_{k})=c \sum_{i=1}^{n}(a_{k})\] |
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\[3N-3-2=3N-5\] |
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\[\int cdx\] |
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\[g(y)-g(x)\] |
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\[t-s\] |
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\[-y-5(1)\] |
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\[q_{eq}=1-p_{eq}\] |
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\[\int \frac{1}{p}dp= \int \frac{z}{a}dt\] |
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\[x^{3}(x-(2x+3)(2x-3))\] |
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\[(x+2y)(x^{2}-2xy+4y^{2})\] |
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\[w_{1}+w_{2}\] |
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\[E/[E,E]\] |
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\[\lim_{x \rightarrow 0}f(x)\] |
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\[\sqrt{2} \sqrt{2}=2\] |
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\[\lim_{n \rightarrow \infty} \frac{2}{n} \sum_{i=1}^{n} \frac{4i^{2}}{n^{2}}\] |
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\[\int_{a}^{b}f(x)dx= \int_{a}^{b}g(x)dx\] |
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\[\sum F_{x}\] |
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\[( \frac{1}{n \pi}- \frac{ \cos(n \pi)}{n \pi})+( \frac{1}{n \pi}- \frac{ \cos(n \pi)}{n \pi})\] |
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\[M=E-e \sin E\] |
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\[f(1.99999)=3.99999\] |
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\[\sin \alpha \sin \beta= \frac{1}{2}[ \cos( \alpha- \beta)- \cos( \alpha+ \beta)]\] |
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\[\int \sum_{j=0}^{ \infty}a_{j}z^{j}dz= \sum_{j=1}^{ \infty} \frac{a_{j-1}}{j}x^{j}\] |
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\[(1-2^{-s})(1+ \frac{1}{2^{s}}+ \frac{1}{3^{s}}+ \frac{1}{4^{s}}+ \frac{1}{5^{s}}+ \ldots)\] |
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\[e^{x}+18x+12\] |
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\[\sum Y_{i}\] |
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\[\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\] |
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\[\frac{-6x}{-6}< \frac{18}{-6}\] |
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\[\frac{1}{ \sqrt{2}}+ \frac{1}{ \sqrt{2}}i\] |
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\[\cos(x-y)= \cos x \cos y+ \sin x \sin y\] |
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\[y \in B\] |
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\[a^{2}+a=a^{2}+a+1-1=-1\] |
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\[\sqrt{7}+2 \sqrt{7}\] |
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\[e_{PVT}\] |
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\[(d-1)(d+1)\] |
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\[\int \frac{dx}{x}+ \int \frac{2}{x+1}dx\] |
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\[\frac{6 \div 2}{10 \div 2}= \frac{3}{5}\] |
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\[\int x \sin xdx\] |
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\[\frac{1}{2} \int_{1}^{5} \cos(u)du\] |
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\[\tan(- \theta)=- \tan \theta\] |
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\[x= \beta\] |
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\[kg\] |
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\[\frac{1}{5}+ \frac{3}{5}= \frac{1+3}{5}= \frac{4}{5}\] |
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\[8+7\] |
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\[( \cos \theta+i \sin \theta)^{n}= \cos n \theta+i \sin n \theta\] |
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\[P_{1}\] |
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\[ds\] |
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\[8z^{7}+24cz^{5}+24c^{2}z^{3}+8cz^{3}+8c^{3}z+8c^{2}z\] |
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\[1=1(1)(1)\] |
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\[a(b+k)=ab+ak\] |
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\[x \rightarrow 0\] |
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\[Im\] |
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\[x_{B5}\] |
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\[\int f(ax)dx= \frac{1}{a} \int f(x)dx\] |
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\[( \frac{a}{b})^{n}= \frac{a^{n}}{b^{n}}\] |
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\[\frac{3}{8}\] |