# LaTeX2HTML 2002-2-1 (1.70) # Associate images original text with physical files. $key = q/displaystyle{frac{{x^4+x^3-4x^2-4x}}{{x(x-1)(x+1)^2}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{x^4+x^3-4x^2-4x}}{{x(x-1)(x+1)^2}}}$ |; $key = q/array{{ccc}2a-1a2a-1a^2+a-2a^2-1a-1a^2+a-1a^2+a-1aarray{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\begin{array}{ccc} 2a-1 & a & 2a-1\\\\ a^2+a-2 & a^2-1 & a-1\\\\ a^2+a-1 & a^2+a-1 & a \end{array}$ |; $key = q/displaystylearray{{lcl}x(u,v)=u,cos(v)y(u,v)=u,sin(v)z(u,v)=1-u;.array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \begin{array}{lcl} x(u,v)&=& u \cos(v)\\\\ y(u,v)&=& u \sin(v)\\\\ z(u,v)&=& 1-u\;. \end{array}$ |; $key = q/displaystyle{frac{{t^2}}{{1-t^4}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{t^2}}{{1-t^4}}}$ |; $key = q/displaystyle{frac{{1}}{{t(t^2+1)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{t(t^2+1)}}}$ |; $key = q/displaystyle{frac{{ln(cos(x))}}{{exp(x+x^2)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{\ln(\cos(x))}}{{\exp(x+x^2)}}}$ |; $key = q/left.vphantom{array{{ccc}111-7-3-995-51array{}right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\left.\vphantom{ \begin{array}{ccc} 1 & 11 & -7\\\\ -3 & -9 & 9\\\\ 5 & -5 & 1 \end{array}}\right]$ |; $key = q/lambda;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\lambda$ |; $key = q/displaystylett{left[left[array{{rrr}1-30100000array{right]right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tt\left[ \left[ \begin{array}{rrr} 1 & -3 & 0\\\\ 1 & 0 & -3 ... ...n{array}{ccc} 3 & 0 & 0\\\\ 0 & 0 & 0\\\\ 0 & 0 & 0 \end{array}\right] \right]$ |; $key = q/displaystyle{frac{{acdotb}}{{2}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{a\cdot b}}{{2}}}$ |; $key = q/displaystyle{frac{{x^2-y}}{{x^2-1}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{x^2-y}}{{x^2-1}}}$ |; $key = q/displaystyle{frac{{a}}{{displaystylefrac{2}{b}}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{a}}{{\displaystyle \frac{2}{b}}}}$ |; $key = q/displaystylett{left[array{{ccc}-a+1000a+2000a-1array{right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tt\left[ \begin{array}{ccc} -a+1 & 0 & 0\\\\ 0 & a+2 & 0\\\\ 0 & 0 & a-1 \end{array}\right]$ |; $key = q/displaystyle{frac{{1}}{{x}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{x}}}$ |; $key = q/left[vphantom{array{{ccc}11a1a1a11array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\left[\vphantom{ \begin{array}{ccc} 1 & 1 & a\\\\ 1 & a & 1\\\\ a & 1 & 1 \end{array}}\right.$ |; $key = q/displaystyle{frac{{sin(x)^2}}{{cos(2x)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{\sin(x)^2}}{{\cos(2x)}}}$ |; $key = q/array{{ccc}11a1a1a11array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\begin{array}{ccc} 1 & 1 & a\\\\ 1 & a & 1\\\\ a & 1 & 1 \end{array}$ |; $key = q/displaystyleleft{vphantom{array{{lcl}x(t)=t,cos(at)t,sin(at)z(t)=1-t;.array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{\vphantom{ \begin{array}{lcl} x(t)&=& t \cos(a t)\\\\ y(t)&=& t \sin(a t)\\\\ z(t)&=& 1-t\;. \end{array}}\right.$ |; $key = q/displaystylesum_{{j=0}}^{{n-1}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{{j=0}}^{{n-1}}$ |; $key = q/int_{a}^{b};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\int_{a}^{b}$ |; $key = q/displaystylelim_{{xrightarrow+infty}}^{};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \lim_{{x\rightarrow +\infty}}^{}$ |; $key = q/displaystylearray{{lcl}x(t)=sin(t)y(t)=cos^3(t)array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \begin{array}{lcl} x(t)&=& \sin(t)\\\\ y(t)&=& \cos^3(t) \end{array}$ |; $key = q/displaystyleint_{{-2}}^{{-1}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{{-2}}^{{-1}}$ |; $key = q/displaystyle{frac{{x+1}}{{x-3}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{x+1}}{{x-3}}}$ |; $key = q/displaystylearray{{llllllr}x+y+az+y+z=-2array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \begin{array}{llllllr} x &+& y &+& az&=&1\\\\ x & +& a y&+& z&=&1 \\\\ ax & +&y &+& z&=&-2 \end{array}$ |; $key = q/left[vphantom{array{{ccc}111-7-3-995-51array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\left[\vphantom{ \begin{array}{ccc} 1 & 11 & -7\\\\ -3 & -9 & 9\\\\ 5 & -5 & 1 \end{array}}\right.$ |; $key = q/displaystyle{frac{{y-1}}{{x^2-1}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{y-1}}{{x^2-1}}}$ |; $key = q/Delta;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Delta$ |; $key = q/displaystyle{frac{{y-1}}{{x+1}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{y-1}}{{x+1}}}$ |; $key = q/square;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\square$ |; $key = q/bullet;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\bullet$ |; $key = q/displaystyle{frac{{x-7}}{{(x-3)^2}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{x-7}}{{(x-3)^2}}}$ |; $key = q/left[vphantom{array{{ccc}2a-1a2a-1a^2+a-2a-1a^2+a-1a^2+a-1aarray{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\left[\vphantom{ \begin{array}{ccc} 2a-1 & a & 2a-1\\\\ a^2+a-2 & a^2-1 & a-1\\\\ a^2+a-1 & a^2+a-1 & a \end{array}}\right.$ |; $key = q/simeq;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\simeq$ |; $key = q/displaystylearray{{ccc}a-12a^3+3a+1-2a^3+a^2+a-1-a-2a+1a^3-2a+1-a^3+2a-1a^3-2a^2+1array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \begin{array}{ccc} a-1 & 2a^3+3a+1 & -2a^3+a^2+a-1\\\\ -a^2+1 & -2a^3+a^2+2a-1 & 2a^3-a^2-2a+1\\\\ a^3-2a+1 & -a^3+2a-1 & a^3-2a^2+1 \end{array}$ |; $key = q/boxtimes;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\boxtimes$ |; $key = q/displaystyleleft[vphantom{array{{ccc}a-12a^3+3a+1-2a^3+a^2+aow_mark>a^3-2a+1-a^3+2a-1a^3-2a^2+1array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left[\vphantom{ \begin{array}{ccc} a-1 & 2a^3+3a+1 & -2a^3+a^2+a... ...+2a-1 & 2a^3-a^2-2a+1\\\\ a^3-2a+1 & -a^3+2a-1 & a^3-2a^2+1 \end{array}}\right.$ |; $key = q/displaystyleint_{0}^{1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{0}^{1}$ |; $key = q/displaystylePhi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Phi$ |; $key = q/displaystyle{frac{{1}}{{xsqrt{1+x^2}}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{x\sqrt{1+x^2}}}}$ |; $key = q/{frac{{1}}{{pi^4}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\frac{{1}}{{\pi^4}}}$ |; $key = q/displaystyleleft{vphantom{array{{lcl}x(t)=sin(132,t)y(t)=cos^3(126,t)array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{\vphantom{ \begin{array}{lcl} x(t)&=& \sin(132 t)\\\\ y(t)&=& \cos^3(126 t) \end{array}}\right.$ |; $key = q/displaystylelim_{{xrightarrow0}}^{};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \lim_{{x\rightarrow 0}}^{}$ |; $key = q/sqrt{{2}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sqrt{{2}}$ |; $key = q/displaystyle{frac{{y-1}}{{x-1}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{y-1}}{{x-1}}}$ |; $key = q/mathbb{Z};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mathbb {Z}$ |; $key = q/{frac{{1}}{{12}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\frac{{1}}{{12}}}$ |; $key = q/displaystyle{frac{{x^3-yx^2-yx+y^2}}{{x^3-yx^2-x+y}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{x^3-yx^2-yx+y^2}}{{x^3-yx^2-x+y}}}$ |; $key = q/displaystyle{frac{{exp(x)^2-exp(x)+1}}{{exp(x)^3+exp(x)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{\exp(x)^2-\exp(x)+1}}{{\exp(x)^3+\exp(x)}}}$ |; $key = q/scriptstylealpha;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\scriptstyle \alpha$ |; $key = q/displaystyle{frac{{1}}{{(x-1)(x+1)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{(x-1)(x+1)}}}$ |; $key = q/displaystylelim_{{x->+infty}}^{};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \lim_{{x->+\infty}}^{}$ |; $key = q/displaystyle{frac{{(x+2)(x-2)}}{{(x-1)(x+1)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{(x+2)(x-2)}}{{(x-1)(x+1)}}}$ |; $key = q/displaystylesum_{{p=1}}^{infty};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{{p=1}}^{\infty}$ |; $key = q/displaystyleleft.vphantom{frac{1+x+y}{(1+x)(1+y)}}right)^{3}_{};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left.\vphantom{ \frac{1+x+y}{(1+x)(1+y)} }\right)^{3}_{}$ |; $key = q/displaystyle{frac{{a}}{{2cdotb}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{a}}{{2\cdot b}}}$ |; $key = q/displaystyleleft.vphantom{frac{x}{1+y},,,frac{y}{1+x}}right);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left.\vphantom{\frac{x}{1+y} , \frac{y}{1+x}}\right)$ |; $key = q/displaystyleleft{vphantom{array{{llllllr}x+y+y+z=-2array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{\vphantom{ \begin{array}{llllllr} x &+& y &+& az&=&1\\\\ x & +& a y&+& z&=&1 \\\\ ax & +&y &+& z&=&-2 \end{array}}\right.$ |; $key = q/displaystylearray{{cccccc}010ldots-a_1ldots-a_{d-1}array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \begin{array}{cccccc} 0&1&0&\ldots&&0 \vdots&\ddots&\ddots&\dd... ...ots&\ddots&0 0&\ldots&&\ldots&0&1 -a_0&-a_1&&\ldots&&-a_{d-1} \end{array}$ |; $key = q/mapsto;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mapsto$ |; $key = q/mathbb{R};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mathbb {R}$ |; $key = q/displaystyleleft{vphantom{array{{lcl}x(u,v)=u,cos(v)u,sin(v)z(u,v)=1-u;.array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{\vphantom{ \begin{array}{lcl} x(u,v)&=& u \cos(v)\\\\ y(u,v)&=& u \sin(v)\\\\ z(u,v)&=& 1-u\;. \end{array}}\right.$ |; $key = q/displaystyle{frac{{x^2}}{{(x-1)(x+1)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{x^2}}{{(x-1)(x+1)}}}$ |; $key = q/displaystyle{frac{{1}}{{2a^4-2a^3-2a^2+2a}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{2a^4-2a^3-2a^2+2a}}}$ |; $key = q/displaystylett{left[array{{rrr}-11101-2-111array{right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tt\left[ \begin{array}{rrr} -1 & 1 & 1\\\\ 0 & 1 & -2\\\\ -1 & 1 & 1 \end{array}\right]$ |; $key = q/array{{ccc}111-7-3-995-51array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\begin{array}{ccc} 1 & 11 & -7\\\\ -3 & -9 & 9\\\\ 5 & -5 & 1 \end{array}$ |; $key = q/_size;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\_size$ |; $key = q/displaystyle{frac{{x}}{{1+y}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{x}}{{1+y}}}$ |; $key = q/displaystyle{frac{{ln(x)}}{{x(x^2+1)^2}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{\ln(x)}}{{x(x^2+1)^2}}}$ |; $key = q/pi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\pi$ |; $key = q/displaystyle{frac{{1}}{{2}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{2}}}$ |; $key = q/displaystyle{frac{{1}}{{1+sin(x)+cos(x)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{1+\sin(x)+\cos(x)}}}$ |; $key = q/displaystyleleft.vphantom{array{{cccccc}010ldotsldots-a_{d-1}array{}right);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left.\vphantom{ \begin{array}{cccccc} 0&1&0&\ldots&&0 \vdots&... ...s&0 0&\ldots&&\ldots&0&1 -a_0&-a_1&&\ldots&&-a_{d-1} \end{array} }\right)$ |; $key = q/displaystylett{left[left[array{{rrr}-1110a+2000a-1array{right]right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tt\left[ \left[ \begin{array}{rrr} -1 & 1 & 1\\\\ 0 & 1 & -2 ... ...}{ccc} -a+1 & 0 & 0\\\\ 0 & a+2 & 0\\\\ 0 & 0 & a-1 \end{array}\right] \right]$ |; $key = q/displaystyleint_{1}^{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{1}^{2}$ |; $key = q/displaystylearray{{lcl}x(t)=sin(132,t)y(t)=cos^3(126,t)array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \begin{array}{lcl} x(t)&=& \sin(132 t)\\\\ y(t)&=& \cos^3(126 t) \end{array}$ |; $key = q/displaystyleint_{0}^{x};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{0}^{x}$ |; $key = q/displaystylesqrt{{cos(x)}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sqrt{{\cos(x)}}$ |; $key = q/epsilon;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\epsilon$ |; $key = q/displaystyleleft(vphantom{array{{cccccc}010ldotsldots-a_{d-1}array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left(\vphantom{ \begin{array}{cccccc} 0&1&0&\ldots&&0 \vdots&... ...s&0 0&\ldots&&\ldots&0&1 -a_0&-a_1&&\ldots&&-a_{d-1} \end{array} }\right.$ |; $key = q/geq;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\geq$ |; $key = q/notin;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\not\in$ |; $key = q/displaystyle{frac{{sin(x)}}{{x}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{\sin(x)}}{{x}}}$ |; $key = q/displaystyleint;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int$ |; $key = q/displaystylearray{{lcl}x(t)=sin(4,t)y(t)=cos^3(6,t)array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \begin{array}{lcl} x(t)&=& \sin(4 t)\\\\ y(t)&=& \cos^3(6 t) \end{array}$ |; $key = q/displaystyle{frac{{t^2-t+1}}{{t^4+t^2}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{t^2-t+1}}{{t^4+t^2}}}$ |; $key = q/displaystyleiint_{D}^{};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \iint_{D}^{}$ |; $key = q/leq;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\leq$ |; $key = q/Phi^{{-1}}_{};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Phi^{{-1}}_{}$ |; $key = q/displaystyle{frac{{y}}{{1+x}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{y}}{{1+x}}}$ |; $key = q/displaystyle{frac{{x^4+x^3-4x^2-4x}}{{x^4+x^3-x^2-x}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{x^4+x^3-4x^2-4x}}{{x^4+x^3-x^2-x}}}$ |; $key = q/displaystyleleft(vphantom{frac{1+x+y}{(1+x)(1+y)}}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left(\vphantom{ \frac{1+x+y}{(1+x)(1+y)} }\right.$ |; $key = q/displaystyleleft.vphantom{array{{ccc}a-12a^3+3a+1-2a^3+a^2+aow_mark>a^3-2a+1-a^3+2a-1a^3-2a^2+1array{}right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left.\vphantom{ \begin{array}{ccc} a-1 & 2a^3+3a+1 & -2a^3+a^2+a... ...+2a-1 & 2a^3-a^2-2a+1\\\\ a^3-2a+1 & -a^3+2a-1 & a^3-2a^2+1 \end{array}}\right]$ |; $key = q/neq;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\neq$ |; $key = q/displaystylearray{{lcl}x(t)=a,cos(t)y(t)=a,sin(t)z(t)=1-a;.array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \begin{array}{lcl} x(t)&=& a \cos(t)\\\\ y(t)&=& a \sin(t)\\\\ z(t)&=& 1-a\;. \end{array}$ |; $key = q/displaystyle{frac{{t^p}}{{p!}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{t^p}}{{p!}}}$ |; $key = q/sqrt{{x^2+y^2}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sqrt{{x^2+y^2}}$ |; $key = q/alpha;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\alpha$ |; $key = q/displaystyle{frac{{1}}{{t^2}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{t^2}}}$ |; $key = q/displaystyle{frac{{1+x+y}}{{(1+x)(1+y)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1+x+y}}{{(1+x)(1+y)}}}$ |; $key = q/displaystyle{frac{{1}}{{x^3+1}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{x^3+1}}}$ |; $key = q/displaystylearray{{lcl}x(t)=t,cos(at)y(t)=t,sin(at)z(t)=1-t;.array{;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \begin{array}{lcl} x(t)&=& t \cos(a t)\\\\ y(t)&=& t \sin(a t)\\\\ z(t)&=& 1-t\;. \end{array}$ |; $key = q/displaystylesqrt{{e^x-1}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sqrt{{e^x-1}}$ |; $key = q/infty;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\infty$ |; $key = q/Phi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Phi$ |; $key = q/displaystyleleft(vphantom{frac{x}{1+y},,,frac{y}{1+x}}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left(\vphantom{\frac{x}{1+y} , \frac{y}{1+x}}\right.$ |; $key = q/displaystyle{frac{{x^2-y}}{{(x-1)(x+1)}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{x^2-y}}{{(x-1)(x+1)}}}$ |; $key = q/displaystyleleft{vphantom{array{{lcl}x(t)=sin(4,t)y(t)=cos^3(6,t)array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{\vphantom{ \begin{array}{lcl} x(t)&=& \sin(4 t)\\\\ y(t)&=& \cos^3(6 t) \end{array}}\right.$ |; $key = q/displaystyleiint_{Delta}^{};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \iint_{\Delta}^{}$ |; $key = q/left.vphantom{array{{ccc}11a1a1a11array{}right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\left.\vphantom{ \begin{array}{ccc} 1 & 1 & a\\\\ 1 & a & 1\\\\ a & 1 & 1 \end{array}}\right]$ |; $key = q/left.vphantom{array{{ccc}2a-1a2a-1a^2+a-2a-1a^2+a-1a^2+a-1aarray{}right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\left.\vphantom{ \begin{array}{ccc} 2a-1 & a & 2a-1\\\\ a^2+a-2 & a^2-1 & a-1\\\\ a^2+a-1 & a^2+a-1 & a \end{array}}\right]$ |; $key = q/sqrt{{-1}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sqrt{{-1}}$ |; $key = q/cup;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\cup$ |; $key = q/displaystyle{frac{{1}}{{displaystyle{a_1+frac{1}{displaystyle{a_2+frac{1}{ddots+displaystyle{frac{1}{a_n}}}}}}}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{1}}{{\displaystyle{a_1+ \frac{1}{\displaystyle{a_2+\frac{1}{\ddots+\displaystyle{\frac{1}{a_n}}}}}}}}}$ |; $key = q/displaystyleleft{vphantom{array{{lcl}x(t)=a,cos(t)l_mark>a,sin(t)z(t)=1-a;.array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{\vphantom{ \begin{array}{lcl} x(t)&=& a \cos(t)\\\\ y(t)&=& a \sin(t)\\\\ z(t)&=& 1-a\;. \end{array}}\right.$ |; $key = q/displaystyleleft{vphantom{array{{lcl}x(t)=sin(t)y(t)=cos^3(t)array{}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{\vphantom{ \begin{array}{lcl} x(t)&=& \sin(t)\\\\ y(t)&=& \cos^3(t) \end{array}}\right.$ |; $key = q/displaystyle{frac{{(x+2)(x+1)(x-2)}}{{x^3+x^2-x-1}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\frac{{(x+2)(x+1)(x-2)}}{{x^3+x^2-x-1}}}$ |; $key = q/displaystyleint_{0}^{{pislash2}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{0}^{{\pi/2}}$ |; $key = q/displaystylelim_{{xrightarrow0^+}}^{};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \lim_{{x\rightarrow 0^+}}^{}$ |; $key = q/in;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\in$ |; 1;