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test2_CROHME2016

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\[t(x)= \sum_{n=0}t_{n} \cos \frac{nx}{R}\]
\[\frac{1}{2}p^{2}+ \frac{1}{2}m^{2}x^{2}+gx^{4}\]
\[a= \frac{A- \sin^{2} \theta_{1}}{ \cos^{2} \theta_{1}}\]
\[\frac{G}{H} \times \frac{G}{H}\]
\[\frac{1}{ \sqrt{N}}\]
\[\cos \beta_{n}\]
\[\int dE\]
\[\cos 2 \gamma\]
\[j \neq 9\]
\[v_{1}+v_{2}+ \ldots+v_{n}=nv_{n+1}\]
\[8=2+2+1+1+1+1\]
\[7_{ \alpha}7_{ \alpha}\]
\[\sum_{a}x_{a}=1\]
\[x^{ \prime}(j)=g(j)x(j)\]
\[n_{1} \neq n_{2} \neq n_{3}\]
\[b= \sqrt{x^{i}x^{i}}\]
\[\sqrt{1+y}\]
\[c_{a}(x_{a})\]
\[c^{4}+c_{0}^{4}+c_{1}^{4}\]
\[y= \cos(2x)\]
\[(xy+yx)/2\]
\[(-1)^{w_{6}+w_{7}+w_{8}+w_{9}}\]
\[f(x)-1+ \sum_{n}x^{n}b_{n}(f)\]
\[x^{i}+dx^{i}\]
\[\cos \frac{(a_{0}-a_{1}) \pi}{2}\]
\[X^{6789}=-X^{6789}\]
\[e>e_{c}\]
\[2^{ \frac{1}{4}}( \frac{5- \sqrt{5}}{5+ \sqrt{5}})^{ \frac{3}{4}}\]
\[x^{8}+ix^{9}\]
\[8+7+7+4=26\]
\[\sin( \frac{2 \pi k}{p})\]
\[x^{6}+ \ldots\]
\[\frac{1}{g}(g-B) \frac{1}{g+B}\]
\[21 \times 20 \times 8 \times 8\]
\[\lim_{t \rightarrow \infty}2f_{0}(t)f_{1}(t)=0\]
\[z^{ \frac{1}{6}} \log z\]
\[f(x)= \sin x\]
\[(ba)^{0}=a^{0}b^{0}=b^{0}a^{0}\]
\[-(X^{0})^{2}+(X^{1})^{2}+(X^{2})^{2}+(X^{3})^{2}+(X^{4})^{2}= \alpha_{B}^{2}\]
\[s(n)= \frac{1}{ \sqrt{2}}( \cos \frac{n \pi}{4}+ \sin \frac{n \pi}{4}) \cos \frac{n \pi}{4}\]
\[\frac{(n+3)n}{(n+2)^{2}(n+1)^{2}}\]
\[f_{x_{1}}(x_{2})=f_{x_{1}x_{2}}\]
\[t= \sum_{a}t_{a}\]
\[\sqrt{ \frac{2}{ \pi}} \cos(t- \frac{3 \pi}{4})\]
\[y^{2}=ax^{4}+4bx^{3}+6cx^{2}+4dx+e\]
\[\frac{2}{3}(3 \pm 4 \sqrt{6}c+4c^{2})\]
\[- \frac{1}{3}+1=- \frac{2}{3}\]
\[N.n\]
\[y^{2}=(x-b_{1})(x-b_{2})(x-b_{3})\]
\[c=c_{1}+c_{2}\]
\[\sqrt{3}( \sqrt{2})\]
\[- \sqrt{2(2- \sqrt{2})}\]
\[\pi_{0} \pi_{0} \pi_{0}\]
\[\sqrt{1-x}\]
\[\lim_{r \rightarrow \infty}f(r)=0\]
\[F(x)= \frac{dx}{(1-x)^{d}}- \frac{1}{(1-x)^{d}}+1\]
\[1_{1}+1_{2}+1_{3}+1_{4}+3 \times 4\]
\[B=- \frac{1}{4} \tan( \frac{p \pi}{2})\]
\[\frac{1}{n}\]
\[1 \neq 2 \neq 3\]
\[x=|a-b|+1+2n\]
\[\sin \gamma L\]
\[-2 \int_{2}^{ \infty} \frac{dy}{ \sqrt{y^{2}-4}} \frac{1}{(y+2 \sigma_{1})^{3}}\]
\[x_{o} \leq x \leq L\]
\[B_{3}-2B_{6}+B_{13}+B_{17}-B_{19}=0\]
\[\log p_{0}\]
\[x-y\]
\[\sum n_{i}\]
\[y^{4}=(x-b_{1})(x-b_{1})^{2}(x-b_{3})^{2}(x-b_{4})^{3}\]
\[x \rightarrow x\]
\[\frac{8m(m+1)}{m+31}\]
\[\sin \phi=2 \sin \frac{ \phi}{2} \cos \frac{ \phi}{2}\]
\[b= \sin \alpha\]
\[c= \frac{3}{2}- \frac{12}{m(m+2)}\]
\[x= \sin^{2}q\]
\[u_{7}=x_{7} \sqrt{x_{4}^{4}+x_{5}^{4}}\]
\[x_{0}^{2}+x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=1\]
\[\exists g \in G\]
\[\sqrt{iz}\]
\[9x9\]
\[+z_{2}^{2}z_{3}+z_{2}^{2}z_{4}+z_{3}^{2}z_{1}+z_{3}^{2}z_{2}+z_{3}^{2}z_{4}\]
\[x_{m}= \sqrt{ \frac{ \sqrt{1+4c^{2}}-1}{2}}\]
\[2.4 \times 1.2\]
\[\frac{1}{ \sqrt{V}}\]
\[\int fg= \int gf\]
\[\log(z \log z)\]
\[r= \sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}}\]
\[-b \leq x(p) \leq b\]
\[\lim q_{n}= \alpha\]
\[x^{2}+y^{2}+(z-bt)((z+at)^{2}-t^{2n+1})=0\]
\[\pm \sqrt{3}\]
\[(1-q_{12}^{2})^{2}(1-q_{13}^{2})^{2}(1-q_{23}^{2})^{2}(1-q_{12}^{2}q_{13}^{2}q_{23}^{2})\]
\[x^{p-3}-x^{p}\]
\[ds^{2}= \frac{1}{2}(-dt^{2}+ \frac{ \tan^{2}t}{1+ \frac{8}{9} \tan^{2}t}dx^{2})\]
\[f_{0}>f>f_{1}\]
\[- \sqrt{2- \sqrt{2}}\]
\[y^{4}=(x-b_{1})^{2}(x-b_{2})^{3}(x-b_{3})^{3}\]
\[\cos \theta X^{6}+ \sin \theta X^{2}\]
\[-2 \log(2) \log(r)\]
\[t \times t=1+t\]