image
imagewidth (px)
46
1.73k
latex_formula
stringlengths
6
300
\[x_{k}xx_{k}+y_{k}yx_{k}\]
\[q_{t}=2q\]
\[\sqrt{48}\]
\[1011111011100101_{2}\]
\[\sin(x+y)= \sin x \cos y+ \cos x \sin y\]
\[R_{o}= \frac{( \frac{ \beta+1}{ \beta})r_{e}+( \beta+2+ \frac{2}{ \beta})r_{o}}{2+ \frac{2}{ \beta}}\]
\[1.379194171\]
\[d^{-7}\]
\[2p\]
\[\log_{e}x\]
\[z^{3}+z=z\]
\[X \leq 15\]
\[\frac{1}{2}t^{2}u(t)\]
\[S_{ \infty}= \lim_{n \rightarrow \infty} \frac{a(1-r^{n})}{1-r}= \frac{a}{1-r}\]
\[v_{7}+v_{3}+v_{4}-v_{8}=0\]
\[\sqrt{32}+ \sqrt{32}\]
\[6778\]
\[\pm \sqrt[x]{b}\]
\[a \div b\]
\[z^{5}+z=z\]
\[y=y \prime\]
\[\sum a_{j}x_{j}\]
\[f(z_{0})= \lim_{z \rightarrow z_{0}}f(z)\]
\[C_{t}=C+C=2C\]
\[x.y\]
\[\sum_{j=1}^{m}a_{j}e_{j}\]
\[\int_{a}^{x}f(x)dx\]
\[\pm \sqrt{x}\]
\[[[S]]\]
\[\frac{1}{25}[y^{2}-8y+16-16]\]
\[x_{1}+x_{2}+ \cdots+x_{n} \neq 0\]
\[\phi( \phi(n))\]
\[\frac{1}{ \sqrt{ \pi}} \sqrt{ \pi}=1\]
\[r \rightarrow \infty\]
\[f_{d}= \frac{A_{max}-A}{A_{max}-A_{min}}\]
\[C_{1}y_{1}+C_{2}y_{2}\]
\[\tan \gamma_{i}\]
\[m \times p\]
\[p \geq 1\]
\[u \geq 0\]
\[a \sqrt{b} \pm c \sqrt{b}=(a \pm c) \sqrt{b}\]
\[p_{1}=-p_{2}+p_{5}-p_{6}\]
\[y<b\]
\[b_{L}\]
\[\sqrt{50}\]
\[\theta \rightarrow 0\]
\[\forall \gamma \in X\]
\[\int \frac{1}{y} \frac{dy}{dx}dx= \int adx\]
\[2x(9x+1)(3x+1)^{3}\]
\[(x \times x) \times(x \times x) \times(x \times x)=x \times x \times x \times x \times x \times x\]
\[|y_{2}-y_{1}|\]
\[2^{n-1}+2^{n-2} \cdots 2+1=2^{n}-1\]
\[e^{2x}\]
\[(a-x)(d-x)-bc=x^{2}-(a+d)x+(ad-bc)\]
\[1 \sqrt{7}+2 \sqrt{7}\]
\[\frac{1}{3}(b-a)(b^{2}+ab+a^{2})\]
\[\cos 4 \theta+i \sin 4 \theta=( \cos \theta+i \sin \theta)^{4}\]
\[9.8\]
\[v_{v}=v \sin \theta\]
\[\pm \sqrt{6}\]
\[X_{fg}\]
\[[A]A\]
\[3.00000003\]
\[\sqrt[3]{x^{2}}\]
\[x^{2}+2xy+y^{2}=(x+y)^{2}\]
\[\frac{e^{a}}{e^{b}}=e^{a-b}\]
\[2m\]
\[q_{1},q_{2}, \ldots,q_{m}\]
\[\sum \pi r^{2}= \pi \sum r^{2}\]
\[\sqrt{a}+ \sqrt{b}\]
\[\frac{1}{6} \int \frac{u^{6}}{2}du+ \frac{1}{6} \int \frac{2u^{5}}{2}\]
\[a^{p}+b^{p}=c^{p}\]
\[\sqrt{7}+2 \sqrt{7}=1 \sqrt{7}+2 \sqrt{7}=3 \sqrt{7}\]
\[\frac{d_{2}}{d_{2}-2}\]
\[a_{0} \ldots a_{n}\]
\[\lim_{n \rightarrow \infty}f_{n}(x)=0\]
\[0=X^{3}+2X^{2}-X+1\]
\[Pa\]
\[\sum b_{n}\]
\[1(1)=(1)( \frac{1}{1})\]
\[C^{ \beta}\]
\[(x^{2}+2x+2)(x^{2}-2x+2)\]
\[Ns\]
\[(( \frac{1}{4}(3)^{4}-3(3)^{2})-( \frac{1}{4}(2)^{4}-3(2)^{2}))\]
\[z \rightarrow-z\]
\[\int f(x)-g(x)dx= \int f(x)dx- \int g(x)dx\]
\[\sqrt{x-16}= \sqrt{7-16}= \sqrt{-9}\]
\[A+A+B+B+C\]
\[p_{1}^{ \beta_{1}}p_{2}^{ \beta 2} \ldots p_{n}^{ \beta n}\]
\[i \neq 1\]
\[0 \leq x \leq 2 \pi\]
\[b^{ \log_{b}X}=X\]
\[a_{11}a_{22}-a_{12}a_{2_{1}}\]
\[\frac{5}{6} \neq \frac{4}{3}\]
\[\cos \theta= \frac{e^{i \theta}+e^{-i \theta}}{2}\]
\[\sin x- \sin y=2 \cos( \frac{x+y}{2}) \sin( \frac{x-y}{2})\]
\[\frac{ \sin( \pi)- \sin(0)}{ \pi-0}=0\]
\[\lim_{x \rightarrow \infty}p_{2}(x)>0\]
\[\lim_{n \rightarrow \infty}n \sin( \frac{2^{ \pi}}{n+1})- \lim_{n \rightarrow \infty}n \frac{2 \pi}{n+1}-2 \pi\]
\[\sin(3x)=-4 \sin^{3}(x)+3 \sin(x)\]