# LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.


$key = q/g;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.gif"
 ALT="$g$">|; 

$key = q/x_1=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.gif"
 ALT="$x_1 = 1$">|; 

$key = q/(1,3);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.gif"
 ALT="$(1,3)$">|; 

$key = q/+infty;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.gif"
 ALT="$+\infty$">|; 

$key = q/m=4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img21.gif"
 ALT="$m=4$">|; 

$key = q/displaystyle6lim_{xrightarrow0^{+}}frac{mbox{sen},(6x)}{6x}=-3k;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.gif"
 ALT="$\displaystyle 6 \lim_{x \rightarrow 0^{+}} \frac{\mbox{sen}   (6x)}{6x} = -3k$">|; 

$key = q/h(x)=frac{f(x)}{g(x)};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.gif"
 ALT="$h(x) = \frac{f(x)}{g(x)}$">|; 

$key = q/displaystylef'(x_0)=lim_{xrightarrowx_0}frac{f(x)-f(x_0)}{x-x_0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.gif"
 ALT="$\displaystyle f'(x_0) = \lim_{x \rightarrow x_0}
\frac{f(x)-f(x_0)}{x-x_0}$">|; 

$key = q/h(x)=|1-f(x)|;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.gif"
 ALT="$h(x) = \vert 1 - f(x)\vert$">|; 

$key = q/displaystyleh'(x)=frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}Rightarrowh'(1)=frac{f'(1)g(1)-f(1)g'(1)}{g(1)^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="481" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.gif"
 ALT="$\displaystyle h'(x) = \frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}
\Rightarrow h'(1) = \frac{f'(1)g(1)-f(1)g'(1)}{g(1)^2} $">|; 

$key = q/x_2=-1slash3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.gif"
 ALT="$x_2 = -1/3$">|; 

$key = q/displaystyleleft(2xe^{2xy}-3y^2right)frac{dy}{dx}=-4x-2ye^{2xy};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.gif"
 ALT="$\displaystyle \left( 2x e^{2xy} - 3 y^2 \right) \frac{dy}{dx} =
-4x - 2ye^{2xy}$">|; 

$key = q/displaystylefrac{dy}{dx}=frac{-4x-2ye^{2xy}}{2xe^{2xy}-3y^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.gif"
 ALT="$\displaystyle \frac{dy}{dx} = \frac{-4x - 2ye^{2xy}}{2x e^{2xy}-3y^2}$">|; 

$key = q/displaystylef'(1)=6(1)-2slash1=4,f(1)=3(1)^2-2(0)=3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.gif"
 ALT="$\displaystyle f'(1)=6(1)-2/1 = 4  ,  f(1) = 3(1)^2-2(0)=3$">|; 

$key = q/f;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.gif"
 ALT="$f$">|; 

$key = q/k;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img30.gif"
 ALT="$k$">|; 

$key = q/displaystylefrac{dy}{dx};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.gif"
 ALT="$\displaystyle \frac{dy}{dx} $">|; 

$key = q/(x,y)=(2,0);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.gif"
 ALT="$(x,y) = (2,0)$">|; 

$key = q/displaystylelim_{xrightarrow+infty}frac{cx^2+d}{x^2}=lim_{xrightarrow+infty}frac{cx^2}{x^2}=c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.gif"
 ALT="$\displaystyle \lim_{x \rightarrow +\infty} \frac{cx^2+d}{x^2}=
\lim_{x\rightarrow +\infty} \frac{cx^2}{x^2} = c $">|; 

$key = q/dxslashdt=1.5mslashs;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.gif"
 ALT="$dx/dt = 1.5 m/s$">|; 

$key = q/d>0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.gif"
 ALT="$d &gt; 0$">|; 

$key = q/displaystylelim_{xrightarrow-infty}frac{cx^2+d}{x^2}=lim_{xrightarrow-infty}frac{cx^2}{x^2}=c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.gif"
 ALT="$\displaystyle \lim_{x \rightarrow -\infty} \frac{cx^2+d}{x^2}=
\lim_{x\rightarrow -\infty} \frac{cx^2}{x^2} = c $">|; 

$key = q/displaystylem=frac{-4(2)-2(0)(1)}{2(2)(1)-3(0)^2}=frac{-8}{4}=-2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.gif"
 ALT="$\displaystyle m = \frac{ -4(2) - 2(0)(1)}{2(2)(1)-3(0)^2} =
\frac{-8}{4} = -2$">|; 

$key = q/displaystyle2e^{2xy}left(xfrac{dy}{dx}+(1)yright)-3y^2frac{dy}{dx}+4x=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.gif"
 ALT="$\displaystyle 2 e^{2xy} \left( x \frac{dy}{dx} + (1) y \right)
- 3 y^2 \frac{dy}{dx} + 4x = 0$">|; 

$key = q/displaystyles=frac{36}{x}Rightarrowfrac{ds}{dt}=frac{ds}{dx}cdotfrac{dx}{dt}=fra}{x^2}cdot(1.5)=frac{-36}{(3)^2}cdot(1.5)=frac{-54}{(3)^2}=-6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="503" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.gif"
 ALT="$\displaystyle s = \frac{36}{x} \Rightarrow \frac{ds}{dt} =
\frac{ds}{dx} \cdot ...
...{-36}{x^2} \cdot (1.5) = \frac{-36}{(3)^2} \cdot (1.5) =
\frac{-54}{(3)^2}= -6$">|; 

$key = q/displaystylef'(x)=3(2x)-frac{2}{x}=frac{6x^2-2}{x};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.gif"
 ALT="$\displaystyle f'(x) = 3 (2x) - \frac{2}{x} = \frac{6x^2-2}{x}$">|; 

$key = q/0<xleq20;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.gif"
 ALT="$0 &lt; x \leq 20 $">|; 

$key = q/displaystylefrac{x}{1.8}=frac{20}{s}Rightarrows=s(x)=frac{20(1.8)}{x}=frac{36}{x};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.gif"
 ALT="$\displaystyle \frac{x}{1.8} = \frac{20}{s} \Rightarrow s = s(x)=
\frac{20(1.8)}{x} = \frac{36}{x}$">|; 

$key = q/displaystylef'(-3)=lim_{xrightarrow-3}frac{(x^2-2x)-((-3)^2-2(-3))}{x-(-3)}=lim_{xrightarrow-3}frac{x^2-2x-15}{x+3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="503" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.gif"
 ALT="$\displaystyle f'(-3) = \lim_{x \rightarrow -3}
\frac{ (x^2-2x)-((-3)^2-2(-3))}{x-(-3)} =
\lim_{x \rightarrow -3} \frac{x^2 - 2x-15}{x+3}$">|; 

$key = q/displaystyleh'(1)=frac{4(1slash4)-3(1slash3)}{(1slash4)^2}=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.gif"
 ALT="$\displaystyle h'(1) = \frac{ 4 (1/4) - 3 (1/3) }{(1/4)^2} = 0$">|; 

$key = q/dsslashdt;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.gif"
 ALT="$ds/dt$">|; 

$key = q/f(x)=3x^2-2ln(x);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.gif"
 ALT="$f(x) = 3 x^2 - 2 \ln(x)$">|; 

$key = q/displaystylelim_{urightarrow0}frac{mbox{sen},(u)}{u}=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.gif"
 ALT="$\displaystyle \lim_{u \rightarrow 0} \frac{\mbox{sen}   (u)}{u} = 1$">|; 

$key = q/displaystylef(x)=frac{cx^2+d}{x^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.gif"
 ALT="$\displaystyle f(x) = \frac{cx^2 + d}{x^2}$">|; 

$key = q/(2,0);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.gif"
 ALT="$(2,0)$">|; 

$key = q/(0-2)slash(3-1)=-1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.gif"
 ALT="$(0-2)/(3-1)=-1$">|; 

$key = q/displaystylef'(-3)=lim_{xrightarrow-3}frac{(x+3)(x-5)}{x+3}=lim_{xrightarrow-3}(x-5)=-3-5=-8;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.gif"
 ALT="$\displaystyle f'(-3) =
\lim_{x \rightarrow -3} \frac{(x+3)(x-5)}{x+3} =
\lim_{x \rightarrow -3} (x-5)= -3 - 5 = -8$">|; 

$key = q/displaystylex=frac{-(-2)pmsqrt{(-2)^2-4(3)(-1)}}{2(3)}=frac{2pmsqrt{16}}{6}=frac{2pm4}{6};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="416" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.gif"
 ALT="$\displaystyle x = \frac{-(-2) \pm \sqrt{(-2)^2-4(3)(-1)}}{2(3)} =
\frac{2 \pm \sqrt{16}}{6} = \frac{2 \pm 4}{6}$">|; 

$key = q/4x-y+3=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.gif"
 ALT="$4x-y + 3 = 0$">|; 

$key = q/(2-1)slash(1-0)=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.gif"
 ALT="$(2-1)/(1-0)=1$">|; 

$key = q/g(x)=1-f(x);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.gif"
 ALT="$g(x) = 1 - f(x)$">|; 

$key = q/y=c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.gif"
 ALT="$y=c$">|; 

$key = q/c>0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.gif"
 ALT="$c &gt; 0$">|; 

$key = q/[-1,3];MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.gif"
 ALT="$[-1,3]$">|; 

$key = q/f'(x_0);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.gif"
 ALT="$f'(x_0)$">|; 

$key = q/x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img62.gif"
 ALT="$x$">|; 

$key = q/displaystylefrac{6x^2-2}{x}=4Leftrightarrow3x^2-1=2xLeftrightarrow3x^2-2x-1=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.gif"
 ALT="$\displaystyle \frac{6x^2-2}{x} = 4 \Leftrightarrow 3x^2 - 1 = 2x
\Leftrightarrow 3x^2 - 2x - 1 = 0$">|; 

$key = q/h'(1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.gif"
 ALT="$h'(1)$">|; 

$key = q/x_0=-3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.gif"
 ALT="$x_0 = -3$">|; 

$key = q/g'(1)=1slash3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.gif"
 ALT="$g'(1) = 1/3$">|; 

$key = q/displaystylelim_{xrightarrow0^{+}}f(x)=f(0)=lim_{xrightarrow0^{-}}f(x);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.gif"
 ALT="$\displaystyle \lim_{x \rightarrow 0^{+} } f(x) = f(0) = \lim_{x
\rightarrow 0^{-}} f(x) $">|; 

$key = q/k=-2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.gif"
 ALT="$k=-2$">|; 

$key = q/displaystylelim_{xrightarrow0^{+}}frac{mbox{sen},(6x)}{x}=-3k=lim_{xrightarrow0^{-}}x^2-3k;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.gif"
 ALT="$\displaystyle \lim_{x \rightarrow 0^{+}} \frac{\mbox{sen}   (6x)}{x} = -3k =
\lim_{x \rightarrow 0^{-} } x^2 - 3k $">|; 

$key = q/f(x);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.gif"
 ALT="$f(x)$">|; 

$key = q/displaystylef(x)=left{array{{lr}displaystylefrac{mbox{sen},(6x)}{x},&mbox{se}x>0x^2-3k,&mbox{se}xleq0array{right.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="80" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.gif"
 ALT="$\displaystyle f(x) = \left\{ \begin{array}{lr}
\displaystyle \frac{\mbox{sen} \...
...x}, &amp; \mbox{se} x &gt; 0 \\\\
x^2 - 3k , &amp; \mbox{se} x \leq 0
\end{array} \right. $">|; 

$key = q/s;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img61.gif"
 ALT="$s$">|; 

$key = q/-infty;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.gif"
 ALT="$-\infty$">|; 

$key = q/displaystyley-0=-2(x-2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.gif"
 ALT="$\displaystyle y - 0 = -2 (x-2)$">|; 

$key = q/displaystylef'(x)=6x-2slashx;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.gif"
 ALT="$\displaystyle f'(x) = 6x - 2/x$">|; 

$key = q/f(x)=x^2-2x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.gif"
 ALT="$f(x) = x^2 - 2x$">|; 

$key = q/displaystyle6=-3kLeftrightarrowk=-2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.gif"
 ALT="$\displaystyle 6 = -3k \Leftrightarrow k = -2$">|; 

$key = q/{{mathbb{R}{};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.gif"
 ALT="${\mathbb{R}}$">|; 

$key = q/x=20-17=3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.gif"
 ALT="$x=20-17=3$">|; 

$key = q/e^{2xy}-y^3+2x^2=9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.gif"
 ALT="$e^{2xy} - y^3 + 2x^2 = 9$">|; 

$key = q/g(1)=1slash4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.gif"
 ALT="$g(1) = 1/4$">|; 

$key = q/-6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.gif"
 ALT="$-6$">|; 

$key = q/displaystylelim_{xrightarrow0}f(x)=lim_{xrightarrow0}frac{cx^2+d}{x^2}=lim_{xrightarrow0}c+frac{d}{x^2}=+infty;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.gif"
 ALT="$\displaystyle \lim_{x \rightarrow 0} f(x) = \lim_{x \rightarrow 0}
\frac{cx^2+d}{x^2} = \lim_{x\rightarrow 0}
c + \frac{d}{x^2} = +\infty$">|; 

$key = q/x=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.gif"
 ALT="$x=0$">|; 

$key = q/(0,1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.gif"
 ALT="$(0,1)$">|; 

1;