# 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|<IMG
 WIDTH="122" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle {\frac{{x^4+x^3-4x^2-4x}}{{x(x-1)(x+1)^2}}}$">|; 

$key = q/array{{ccc}2a-1<col_mark>a<col_mark>2a-1<row_mark>a^2+a-2<col_mark>a^2-1<col_mark>a-1<row_mark>a^2+a-1<col_mark>a^2+a-1<col_mark>aarray{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$ \begin{array}{ccc}
2a-1 &amp; a &amp; 2a-1\\\\
a^2+a-2 &amp; a^2-1 &amp; a-1\\\\
a^2+a-1 &amp; a^2+a-1 &amp; a
\end{array}$">|; 

$key = q/displaystylearray{{lcl}x(u,v)<col_mark>=<col_mark>u,cos(v)<row_mark>y(u,v)<col_m>=<col_mark>u,sin(v)<row_mark>z(u,v)<col_mark>=<col_mark>1-u;.array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle \begin{array}{lcl}
x(u,v)&amp;=&amp; u \cos(v)\\\\
y(u,v)&amp;=&amp; u \sin(v)\\\\
z(u,v)&amp;=&amp; 1-u\;.
\end{array}$">|; 

$key = q/displaystyle{frac{{t^2}}{{1-t^4}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\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|<IMG
 WIDTH="61" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\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|<IMG
 WIDTH="80" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle {\frac{{\ln(\cos(x))}}{{\exp(x+x^2)}}}$">|; 

$key = q/left.vphantom{array{{ccc}1<col_mark>11<col_mark>-7<row_mark>-3<col_mark>-9<col_mark>9<row_mark>5<col_mark>-5<col_mark>1array{}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$ \left.\vphantom{
\begin{array}{ccc}
1 &amp; 11 &amp; -7\\\\
-3 &amp; -9 &amp; 9\\\\
5 &amp; -5 &amp; 1
\end{array}}\right]$">|; 

$key = q/lambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$ \lambda$">|; 

$key = q/displaystylett{left[left[array{{rrr}1<col_mark>-3<col_mark>0<row_mark>1<col_markmark>0<col_mark>0<row_mark>0<col_mark>0<col_mark>0array{right]right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle \tt\left[ \left[
\begin{array}{rrr}
1 &amp; -3 &amp; 0\\\\
1 &amp; 0 &amp; -3 ...
...n{array}{ccc}
3 &amp; 0 &amp; 0\\\\
0 &amp; 0 &amp; 0\\\\
0 &amp; 0 &amp; 0
\end{array}\right]
\right]$">|; 

$key = q/displaystyle{frac{{acdotb}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\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|<IMG
 WIDTH="45" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\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|<IMG
 WIDTH="19" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$\displaystyle {\frac{{a}}{{\displaystyle \frac{2}{b}}}}$">|; 

$key = q/displaystylett{left[array{{ccc}-a+1<col_mark>0<col_mark>0<row_mark>0<col_mark>a+2<col_mark>0<row_mark>0<col_mark>0<col_mark>a-1array{right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\displaystyle \tt\left[
\begin{array}{ccc}
-a+1 &amp; 0 &amp; 0\\\\
0 &amp; a+2 &amp; 0\\\\
0 &amp; 0 &amp; a-1
\end{array}\right]$">|; 

$key = q/displaystyle{frac{{1}}{{x}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$\displaystyle {\frac{{1}}{{x}}}$">|; 

$key = q/left[vphantom{array{{ccc}1<col_mark>1<col_mark>a<row_mark>1<col_mark>a<col_mark>1<row_mark>a<col_mark>1<col_mark>1array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$ \left[\vphantom{
\begin{array}{ccc}
1 &amp; 1 &amp; a\\\\
1 &amp; a &amp; 1\\\\
a &amp; 1 &amp; 1
\end{array}}\right.$">|; 

$key = q/displaystyle{frac{{sin(x)^2}}{{cos(2x)}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle {\frac{{\sin(x)^2}}{{\cos(2x)}}}$">|; 

$key = q/array{{ccc}1<col_mark>1<col_mark>a<row_mark>1<col_mark>a<col_mark>1<row_mark>a<col_mark>1<col_mark>1array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$ \begin{array}{ccc}
1 &amp; 1 &amp; a\\\\
1 &amp; a &amp; 1\\\\
a &amp; 1 &amp; 1
\end{array}$">|; 

$key = q/displaystyleleft{vphantom{array{{lcl}x(t)<col_mark>=<col_mark>t,cos(at)<row_mark_mark>t,sin(at)<row_mark>z(t)<col_mark>=<col_mark>1-t;.array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\displaystyle \left\{\vphantom{
\begin{array}{lcl}
x(t)&amp;=&amp; t \cos(a t)\\\\
y(t)&amp;=&amp; t \sin(a t)\\\\
z(t)&amp;=&amp; 1-t\;.
\end{array}}\right.$">|; 

$key = q/displaystylesum_{{j=0}}^{{n-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle \sum_{{j=0}}^{{n-1}}$">|; 

$key = q/int_{a}^{b};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$ \int_{a}^{b}$">|; 

$key = q/displaystylelim_{{xrightarrow+infty}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$\displaystyle \lim_{{x\rightarrow +\infty}}^{}$">|; 

$key = q/displaystylearray{{lcl}x(t)<col_mark>=<col_mark>sin(t)<row_mark>y(t)<col_mark>=<col_mark>cos^3(t)array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle \begin{array}{lcl}
x(t)&amp;=&amp; \sin(t)\\\\
y(t)&amp;=&amp; \cos^3(t)
\end{array}$">|; 

$key = q/displaystyleint_{{-2}}^{{-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\displaystyle \int_{{-2}}^{{-1}}$">|; 

$key = q/displaystyle{frac{{x+1}}{{x-3}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle {\frac{{x+1}}{{x-3}}}$">|; 

$key = q/displaystylearray{{llllllr}x<col_mark>+<col_mark>y<col_mark>+<col_mark>az<col_mamark>+<col_mark>y<col_mark>+<col_mark>z<col_mark>=<col_mark>-2array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle \begin{array}{llllllr}
x &amp;+&amp; y &amp;+&amp; az&amp;=&amp;1\\\\
x &amp; +&amp; a y&amp;+&amp; z&amp;=&amp;1 \\\\
ax &amp; +&amp;y &amp;+&amp; z&amp;=&amp;-2
\end{array}$">|; 

$key = q/left[vphantom{array{{ccc}1<col_mark>11<col_mark>-7<row_mark>-3<col_mark>-9<col_mark>9<row_mark>5<col_mark>-5<col_mark>1array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$ \left[\vphantom{
\begin{array}{ccc}
1 &amp; 11 &amp; -7\\\\
-3 &amp; -9 &amp; 9\\\\
5 &amp; -5 &amp; 1
\end{array}}\right.$">|; 

$key = q/displaystyle{frac{{y-1}}{{x^2-1}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle {\frac{{y-1}}{{x^2-1}}}$">|; 

$key = q/Delta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$ \Delta$">|; 

$key = q/displaystyle{frac{{y-1}}{{x+1}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\displaystyle {\frac{{y-1}}{{x+1}}}$">|; 

$key = q/square;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$ \square$">|; 

$key = q/bullet;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ \bullet$">|; 

$key = q/displaystyle{frac{{x-7}}{{(x-3)^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\displaystyle {\frac{{x-7}}{{(x-3)^2}}}$">|; 

$key = q/left[vphantom{array{{ccc}2a-1<col_mark>a<col_mark>2a-1<row_mark>a^2+a-2<col_markl_mark>a-1<row_mark>a^2+a-1<col_mark>a^2+a-1<col_mark>aarray{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$ \left[\vphantom{
\begin{array}{ccc}
2a-1 &amp; a &amp; 2a-1\\\\
a^2+a-2 &amp; a^2-1 &amp; a-1\\\\
a^2+a-1 &amp; a^2+a-1 &amp; a
\end{array}}\right.$">|; 

$key = q/simeq;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$ \simeq$">|; 

$key = q/displaystylearray{{ccc}a-1<col_mark>2a^3+3a+1<col_mark>-2a^3+a^2+a-1<row_mark>-a-2a+1<row_mark>a^3-2a+1<col_mark>-a^3+2a-1<col_mark>a^3-2a^2+1array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="363" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle \begin{array}{ccc}
a-1 &amp; 2a^3+3a+1 &amp; -2a^3+a^2+a-1\\\\
-a^2+1 &amp; -2a^3+a^2+2a-1 &amp; 2a^3-a^2-2a+1\\\\
a^3-2a+1 &amp; -a^3+2a-1 &amp; a^3-2a^2+1
\end{array}$">|; 

$key = q/boxtimes;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$ \boxtimes$">|; 

$key = q/displaystyleleft[vphantom{array{{ccc}a-1<col_mark>2a^3+3a+1<col_mark>-2a^3+a^2+aow_mark>a^3-2a+1<col_mark>-a^3+2a-1<col_mark>a^3-2a^2+1array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\displaystyle \left[\vphantom{
\begin{array}{ccc}
a-1 &amp; 2a^3+3a+1 &amp; -2a^3+a^2+a...
...+2a-1 &amp; 2a^3-a^2-2a+1\\\\
a^3-2a+1 &amp; -a^3+2a-1 &amp; a^3-2a^2+1
\end{array}}\right.$">|; 

$key = q/displaystyleint_{0}^{1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$\displaystyle \int_{0}^{1}$">|; 

$key = q/displaystylePhi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle \Phi$">|; 

$key = q/displaystyle{frac{{1}}{{xsqrt{1+x^2}}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$\displaystyle {\frac{{1}}{{x\sqrt{1+x^2}}}}$">|; 

$key = q/{frac{{1}}{{pi^4}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$ {\frac{{1}}{{\pi^4}}}$">|; 

$key = q/displaystyleleft{vphantom{array{{lcl}x(t)<col_mark>=<col_mark>sin(132,t)<row_mark>y(t)<col_mark>=<col_mark>cos^3(126,t)array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\displaystyle \left\{\vphantom{
\begin{array}{lcl}
x(t)&amp;=&amp; \sin(132 t)\\\\
y(t)&amp;=&amp; \cos^3(126 t)
\end{array}}\right.$">|; 

$key = q/displaystylelim_{{xrightarrow0}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$\displaystyle \lim_{{x\rightarrow 0}}^{}$">|; 

$key = q/sqrt{{2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$ \sqrt{{2}}$">|; 

$key = q/displaystyle{frac{{y-1}}{{x-1}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\displaystyle {\frac{{y-1}}{{x-1}}}$">|; 

$key = q/mathbb{Z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$ \mathbb {Z}$">|; 

$key = q/{frac{{1}}{{12}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$ {\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|<IMG
 WIDTH="120" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\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|<IMG
 WIDTH="139" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\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|<IMG
 WIDTH="11" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\scriptstyle \alpha$">|; 

$key = q/displaystyle{frac{{1}}{{(x-1)(x+1)}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle {\frac{{1}}{{(x-1)(x+1)}}}$">|; 

$key = q/displaystylelim_{{x->+infty}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle \lim_{{x-&gt;+\infty}}^{}$">|; 

$key = q/displaystyle{frac{{(x+2)(x-2)}}{{(x-1)(x+1)}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\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|<IMG
 WIDTH="25" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\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|<IMG
 WIDTH="23" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\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|<IMG
 WIDTH="32" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\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|<IMG
 WIDTH="17" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\displaystyle \left.\vphantom{\frac{x}{1+y} , \frac{y}{1+x}}\right)$">|; 

$key = q/displaystyleleft{vphantom{array{{llllllr}x<col_mark>+<col_mark>y<col_mark>+<col_col_mark>y<col_mark>+<col_mark>z<col_mark>=<col_mark>-2array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\displaystyle \left\{\vphantom{ \begin{array}{llllllr}
x &amp;+&amp; y &amp;+&amp; az&amp;=&amp;1\\\\
x &amp; +&amp; a y&amp;+&amp; z&amp;=&amp;1 \\\\
ax &amp; +&amp;y &amp;+&amp; z&amp;=&amp;-2
\end{array}}\right.$">|; 

$key = q/displaystylearray{{cccccc}0<col_mark>1<col_mark>0<col_mark>ldots<col_mark><col_mmark>-a_1<col_mark><col_mark>ldots<col_mark><col_mark>-a_{d-1}array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="152" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$\displaystyle \begin{array}{cccccc} 0&amp;1&amp;0&amp;\ldots&amp;&amp;0  \vdots&amp;\ddots&amp;\ddots&amp;\dd...
...ots&amp;\ddots&amp;0  0&amp;\ldots&amp;&amp;\ldots&amp;0&amp;1  -a_0&amp;-a_1&amp;&amp;\ldots&amp;&amp;-a_{d-1} \end{array}$">|; 

$key = q/mapsto;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$ \mapsto$">|; 

$key = q/mathbb{R};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$ \mathbb {R}$">|; 

$key = q/displaystyleleft{vphantom{array{{lcl}x(u,v)<col_mark>=<col_mark>u,cos(v)<row_marmark>u,sin(v)<row_mark>z(u,v)<col_mark>=<col_mark>1-u;.array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle \left\{\vphantom{
\begin{array}{lcl}
x(u,v)&amp;=&amp; u \cos(v)\\\\
y(u,v)&amp;=&amp; u \sin(v)\\\\
z(u,v)&amp;=&amp; 1-u\;.
\end{array}}\right.$">|; 

$key = q/displaystyle{frac{{x^2}}{{(x-1)(x+1)}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\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|<IMG
 WIDTH="141" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\displaystyle {\frac{{1}}{{2a^4-2a^3-2a^2+2a}}}$">|; 

$key = q/displaystylett{left[array{{rrr}-1<col_mark>1<col_mark>1<row_mark>0<col_mark>1<col_mark>-2<row_mark>-1<col_mark>1<col_mark>1array{right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle \tt\left[
\begin{array}{rrr}
-1 &amp; 1 &amp; 1\\\\
0 &amp; 1 &amp; -2\\\\
-1 &amp; 1 &amp; 1
\end{array}\right]$">|; 

$key = q/array{{ccc}1<col_mark>11<col_mark>-7<row_mark>-3<col_mark>-9<col_mark>9<row_mark>5<col_mark>-5<col_mark>1array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$ \begin{array}{ccc}
1 &amp; 11 &amp; -7\\\\
-3 &amp; -9 &amp; 9\\\\
5 &amp; -5 &amp; 1
\end{array}$">|; 

$key = q/_size;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$ \_size$">|; 

$key = q/displaystyle{frac{{x}}{{1+y}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\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|<IMG
 WIDTH="72" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$\displaystyle {\frac{{\ln(x)}}{{x(x^2+1)^2}}}$">|; 

$key = q/pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$ \pi$">|; 

$key = q/displaystyle{frac{{1}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\displaystyle {\frac{{1}}{{2}}}$">|; 

$key = q/displaystyle{frac{{1}}{{1+sin(x)+cos(x)}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$\displaystyle {\frac{{1}}{{1+\sin(x)+\cos(x)}}}$">|; 

$key = q/displaystyleleft.vphantom{array{{cccccc}0<col_mark>1<col_mark>0<col_mark>ldots<c_1<col_mark><col_mark>ldots<col_mark><col_mark>-a_{d-1}array{}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="152" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\displaystyle \left.\vphantom{ \begin{array}{cccccc} 0&amp;1&amp;0&amp;\ldots&amp;&amp;0  \vdots&amp;...
...s&amp;0  0&amp;\ldots&amp;&amp;\ldots&amp;0&amp;1  -a_0&amp;-a_1&amp;&amp;\ldots&amp;&amp;-a_{d-1} \end{array} }\right)$">|; 

$key = q/displaystylett{left[left[array{{rrr}-1<col_mark>1<col_mark>1<row_mark>0<col_mark>a+2<col_mark>0<row_mark>0<col_mark>0<col_mark>a-1array{right]right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle \tt\left[ \left[
\begin{array}{rrr}
-1 &amp; 1 &amp; 1\\\\
0 &amp; 1 &amp; -2 ...
...}{ccc}
-a+1 &amp; 0 &amp; 0\\\\
0 &amp; a+2 &amp; 0\\\\
0 &amp; 0 &amp; a-1
\end{array}\right]
\right]$">|; 

$key = q/displaystyleint_{1}^{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\displaystyle \int_{1}^{2}$">|; 

$key = q/displaystylearray{{lcl}x(t)<col_mark>=<col_mark>sin(132,t)<row_mark>y(t)<col_mark>=<col_mark>cos^3(126,t)array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle \begin{array}{lcl}
x(t)&amp;=&amp; \sin(132 t)\\\\
y(t)&amp;=&amp; \cos^3(126 t)
\end{array}$">|; 

$key = q/displaystyleint_{0}^{x};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle \int_{0}^{x}$">|; 

$key = q/displaystylesqrt{{cos(x)}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$\displaystyle \sqrt{{\cos(x)}}$">|; 

$key = q/epsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$ \epsilon$">|; 

$key = q/displaystyleleft(vphantom{array{{cccccc}0<col_mark>1<col_mark>0<col_mark>ldots<c_1<col_mark><col_mark>ldots<col_mark><col_mark>-a_{d-1}array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="152" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$\displaystyle \left(\vphantom{ \begin{array}{cccccc} 0&amp;1&amp;0&amp;\ldots&amp;&amp;0  \vdots&amp;...
...s&amp;0  0&amp;\ldots&amp;&amp;\ldots&amp;0&amp;1  -a_0&amp;-a_1&amp;&amp;\ldots&amp;&amp;-a_{d-1} \end{array} }\right.$">|; 

$key = q/geq;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$ \geq$">|; 

$key = q/notin;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$ \not\in$">|; 

$key = q/displaystyle{frac{{sin(x)}}{{x}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle {\frac{{\sin(x)}}{{x}}}$">|; 

$key = q/displaystyleint;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle \int$">|; 

$key = q/displaystylearray{{lcl}x(t)<col_mark>=<col_mark>sin(4,t)<row_mark>y(t)<col_mark>=<col_mark>cos^3(6,t)array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\displaystyle \begin{array}{lcl}
x(t)&amp;=&amp; \sin(4 t)\\\\
y(t)&amp;=&amp; \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|<IMG
 WIDTH="65" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle {\frac{{t^2-t+1}}{{t^4+t^2}}}$">|; 

$key = q/displaystyleiint_{D}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$\displaystyle \iint_{D}^{}$">|; 

$key = q/leq;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$ \leq$">|; 

$key = q/Phi^{{-1}}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$ \Phi^{{-1}}_{}$">|; 

$key = q/displaystyle{frac{{y}}{{1+x}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\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|<IMG
 WIDTH="122" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\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|<IMG
 WIDTH="17" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{1+x+y}{(1+x)(1+y)} }\right.$">|; 

$key = q/displaystyleleft.vphantom{array{{ccc}a-1<col_mark>2a^3+3a+1<col_mark>-2a^3+a^2+aow_mark>a^3-2a+1<col_mark>-a^3+2a-1<col_mark>a^3-2a^2+1array{}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle \left.\vphantom{
\begin{array}{ccc}
a-1 &amp; 2a^3+3a+1 &amp; -2a^3+a^2+a...
...+2a-1 &amp; 2a^3-a^2-2a+1\\\\
a^3-2a+1 &amp; -a^3+2a-1 &amp; a^3-2a^2+1
\end{array}}\right]$">|; 

$key = q/neq;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$ \neq$">|; 

$key = q/displaystylearray{{lcl}x(t)<col_mark>=<col_mark>a,cos(t)<row_mark>y(t)<col_mark>=<col_mark>a,sin(t)<row_mark>z(t)<col_mark>=<col_mark>1-a;.array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle \begin{array}{lcl}
x(t)&amp;=&amp; a \cos(t)\\\\
y(t)&amp;=&amp; a \sin(t)\\\\
z(t)&amp;=&amp; 1-a\;.
\end{array}$">|; 

$key = q/displaystyle{frac{{t^p}}{{p!}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\displaystyle {\frac{{t^p}}{{p!}}}$">|; 

$key = q/sqrt{{x^2+y^2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$ \sqrt{{x^2+y^2}}$">|; 

$key = q/alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$ \alpha$">|; 

$key = q/displaystyle{frac{{1}}{{t^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\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|<IMG
 WIDTH="95" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\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|<IMG
 WIDTH="45" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle {\frac{{1}}{{x^3+1}}}$">|; 

$key = q/displaystylearray{{lcl}x(t)<col_mark>=<col_mark>t,cos(at)<row_mark>y(t)<col_mark>=<col_mark>t,sin(at)<row_mark>z(t)<col_mark>=<col_mark>1-t;.array{;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle \begin{array}{lcl}
x(t)&amp;=&amp; t \cos(a t)\\\\
y(t)&amp;=&amp; t \sin(a t)\\\\
z(t)&amp;=&amp; 1-t\;.
\end{array}$">|; 

$key = q/displaystylesqrt{{e^x-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\displaystyle \sqrt{{e^x-1}}$">|; 

$key = q/infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$ \infty$">|; 

$key = q/Phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$ \Phi$">|; 

$key = q/displaystyleleft(vphantom{frac{x}{1+y},,,frac{y}{1+x}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\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|<IMG
 WIDTH="95" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle {\frac{{x^2-y}}{{(x-1)(x+1)}}}$">|; 

$key = q/displaystyleleft{vphantom{array{{lcl}x(t)<col_mark>=<col_mark>sin(4,t)<row_mark>y(t)<col_mark>=<col_mark>cos^3(6,t)array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$\displaystyle \left\{\vphantom{
\begin{array}{lcl}
x(t)&amp;=&amp; \sin(4 t)\\\\
y(t)&amp;=&amp; \cos^3(6 t)
\end{array}}\right.$">|; 

$key = q/displaystyleiint_{Delta}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\displaystyle \iint_{\Delta}^{}$">|; 

$key = q/left.vphantom{array{{ccc}1<col_mark>1<col_mark>a<row_mark>1<col_mark>a<col_mark>1<row_mark>a<col_mark>1<col_mark>1array{}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$ \left.\vphantom{
\begin{array}{ccc}
1 &amp; 1 &amp; a\\\\
1 &amp; a &amp; 1\\\\
a &amp; 1 &amp; 1
\end{array}}\right]$">|; 

$key = q/left.vphantom{array{{ccc}2a-1<col_mark>a<col_mark>2a-1<row_mark>a^2+a-2<col_markl_mark>a-1<row_mark>a^2+a-1<col_mark>a^2+a-1<col_mark>aarray{}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$ \left.\vphantom{
\begin{array}{ccc}
2a-1 &amp; a &amp; 2a-1\\\\
a^2+a-2 &amp; a^2-1 &amp; a-1\\\\
a^2+a-1 &amp; a^2+a-1 &amp; a
\end{array}}\right]$">|; 

$key = q/sqrt{{-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$ \sqrt{{-1}}$">|; 

$key = q/cup;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$ \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|<IMG
 WIDTH="130" HEIGHT="158" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\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)<col_mark>=<col_mark>a,cos(t)<row_mark>l_mark>a,sin(t)<row_mark>z(t)<col_mark>=<col_mark>1-a;.array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle \left\{\vphantom{
\begin{array}{lcl}
x(t)&amp;=&amp; a \cos(t)\\\\
y(t)&amp;=&amp; a \sin(t)\\\\
z(t)&amp;=&amp; 1-a\;.
\end{array}}\right.$">|; 

$key = q/displaystyleleft{vphantom{array{{lcl}x(t)<col_mark>=<col_mark>sin(t)<row_mark>y(t)<col_mark>=<col_mark>cos^3(t)array{}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\displaystyle \left\{\vphantom{
\begin{array}{lcl}
x(t)&amp;=&amp; \sin(t)\\\\
y(t)&amp;=&amp; \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|<IMG
 WIDTH="139" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\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|<IMG
 WIDTH="37" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$\displaystyle \int_{0}^{{\pi/2}}$">|; 

$key = q/displaystylelim_{{xrightarrow0^+}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle \lim_{{x\rightarrow 0^+}}^{}$">|; 

$key = q/in;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$ \in$">|; 

1;

