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


$key = q/a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$a$">|; 

$key = q/displaystylelim_{yrightarrow3}frac{y-3}{sqrt{y+1}-2}=lim_{yrightarrow3}frac{y-3}y+1}+2)}{(y+1)-4}=lim_{yrightarrow3}sqrt{y+1}+2=sqrt{3+1}+2=4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="865" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\displaystyle \lim_{y\rightarrow 3} \frac{y-3}{\sqrt{y+1}  -2} =
\lim_{y\righ...
...{y+1}  +2)}{(y+1)-4} =
\lim_{y\rightarrow 3} \sqrt{y+1} +2 = \sqrt{3+1}+2 = 4$">|; 

$key = q/xrightarrow-infty;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$x \rightarrow -\infty$">|; 

$key = q/displaystyleLongrightarrow2x-ycos(xy)=(2y+xcos(xy))frac{dy}{dx}Rightarrowfrac{dy}{dx}=frac{2x-ycos(xy)}{2y+xcos(xy)};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="498" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle
\Longrightarrow 2x- y \cos(xy) = (2y + x \cos(xy))\frac{dy}{dx} \Rightarrow
\frac{dy}{dx} = \frac{2x-y\cos(xy)}{2y + x \cos(xy)}$">|; 

$key = q/y=e^{x^3+3sqrt{x}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$y = e^{x^3 + 3 \sqrt{x}}$">|; 

$key = q/displaystylelim_{yrightarrow3}frac{y-3}{sqrt{y+1}-2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\displaystyle \lim_{y \rightarrow 3} \frac{y-3}{\sqrt{y+1}  -2}$">|; 

$key = q/x^2-9geq0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$x^2-9 \geq 0$">|; 

$key = q/displaystylesqrt{x^2}geqsqrt{9}Leftrightarrow|x|geq3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\displaystyle \sqrt{x^2} \geq \sqrt{9} \Leftrightarrow
\vert x\vert \geq 3$">|; 

$key = q/y=8;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$y=8$">|; 

$key = q/y=x^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$y = x^2$">|; 

$key = q/displaystylef(1)=5(1)^2-3sqrt[3]{1}=5-3=2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\displaystyle f(1) = 5(1)^2 - 3\sqrt[3]{1} = 5-3 = 2$">|; 

$key = q/x=sqrt{pi};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$x = \sqrt{\pi}$">|; 

$key = q/y(t);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$y(t)$">|; 

$key = q/displaystylef(x)=5x^2-3x^{1slash3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\displaystyle f(x) = 5x^2 - 3 x^{1/3}$">|; 

$key = q/displaystyle2x=2yfrac{dy}{dx}+cos(xy)left((1)y+xfrac{dy}{dx}right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle 2x = 2y \frac{dy}{dx} + \cos(xy) \left(
(1)y + x \frac{dy}{dx} \right)$">|; 

$key = q/displaystylef'(1)=10(1)-frac{1}{sqrt[3]{(1)^2}}=10-1=9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle f'(1) = 10(1) - \frac{1}{\sqrt[3]{(1)^2}} = 10-1=9$">|; 

$key = q/f;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$f$">|; 

$key = q/f(3)=|3^2-9|-6=-6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$f(3) = \vert 3^2-9\vert-6=-6$">|; 

$key = q/displaystylef(x)=-(x^2-9)-6=3-x^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle f(x) = -(x^2-9)-6 = 3-x^2$">|; 

$key = q/displaystyle2sfrac{ds}{dt}=2xfrac{dx}{dt}+2yfrac{dy}{dt};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle 2 s \frac{ds}{dt} = 2x \frac{dx}{dt} + 2y \frac{dy}{dt}$">|; 

$key = q/displaystylefrac{dy}{dx}=e^{x^3+3sqrt{x}}(3x^2+(3slash2)x^{-1slash2})=e^{x^3+3sqrt{x}}left(3x^2+frac{3}{2sqrt{x}}right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="448" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\displaystyle \frac{dy}{dx} = e^{x^3+3\sqrt{x}}(3x^2 + (3/2) x^{-1/2})=
e^{x^3+3\sqrt{x}}\left(3x^2 + \frac{3}{2\sqrt{x}}\right)$">|; 

$key = q/displaystyleRightarrowfrac{dy}{dt}=frac{(10)(20)+(8)(50)}{6}=frac{600}{6}=100;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \Rightarrow \frac{dy}{dt} = \frac{(10)(20)+(8)(50)}{6}
= \frac{600}{6} = 100$">|; 

$key = q/displaystylef(x)=frac{2+ln(3x)}{3+x^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\displaystyle f(x) = \frac{2 + \ln(3x)}{3 + x^2}$">|; 

$key = q/x^2geq9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$x^2 \geq 9$">|; 

$key = q/displaystylef'(x)=5(2)x-3(1slash3)x^{-2slash3}=10x-frac{1}{x^{2slash3}}=10x-frac{1}{sqrt[3]{x^2}},xneq0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="495" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle f'(x) = 5(2)x - 3(1/3)x^{-2/3} = 10x - \frac{1}{x^{2/3}}=
10x - \frac{1}{\sqrt[3]{x^2}}  ,  x \neq 0$">|; 

$key = q/f(sqrt{pi})=sqrt{pi};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$f(\sqrt{\pi})=\sqrt{\pi}$">|; 

$key = q/displaystylelim_{xrightarrow3^{+}}frac{f(x)-f(3)}{x-3}=lim_{xrightarrow3^{+}}fraarrow3^{+}}frac{x^2-9}{x-3}=lim_{xrightarrow3^{+}}(x+3)=3+3=6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="638" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle \lim_{x \rightarrow 3^{+}} \frac{f(x)-f(3)}{x-3} =
\lim_{x \right...
...tarrow 3^{+}} \frac{x^2-9}{x-3} =
\lim_{x \rightarrow 3^{+}} (x+3) = 3 + 3 = 6$">|; 

$key = q/t;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$t$">|; 

$key = q/x^2=y^2+mbox{sen},(xy);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$x^2 = y^2 + \mbox{sen}   (xy)$">|; 

$key = q/n;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$n$">|; 

$key = q/dyslashdx;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$dy/dx$">|; 

$key = q/f'(1slash3);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$f'(1/3)$">|; 

$key = q/displaystylelim_{xrightarrow3^{-}}frac{f(x)-f(3)}{x-3}=lim_{xrightarrow3^{-}}frac{3-x^2-(-6)}{x-3}=lim_{xrightarrow3^{-}}frac{9-x^2}{x-3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="425" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\displaystyle \lim_{x \rightarrow 3^{-}} \frac{f(x)-f(3)}{x-3} =
\lim_{x \rightarrow 3^{-}} \frac{3-x^2-(-6)}{x-3} =
\lim_{x \rightarrow 3^{-}} \frac{9-x^2}{x-3}$">|; 

$key = q/displaystylefrac{dx^2}{dx}=frac{d}{dx}left[y^2+mbox{sen},(xy)right];MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle \frac{dx^2}{dx} = \frac{d}{dx} \left[y^2 + \mbox{sen}   (xy) \right]$">|; 

$key = q/s(t);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$s(t)$">|; 

$key = q/9-x^2=-(x^2-9)=-(x+3)(x-3);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$9 - x^2 = -(x^2-9)=-(x+3)(x-3)$">|; 

$key = q/xrightarrow+infty;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$x \rightarrow + \infty$">|; 

$key = q/displaystylef'(x)=frac{(3+x^2)(2+ln(3x))'-(3+x^2)'(2+ln(3x))}{(3+x^2)^2}=frac{(3^2(2+ln(3x))}{x(3+x^2)^2}=frac{3-3x^2-2x^2ln(3x)}{x(3+x^2)^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="1121" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\displaystyle f'(x) = \frac{(3+x^2)(2+\ln(3x))' - (3+x^2)'(2+\ln(3x))}
{(3+x^2)...
...^2) - 2x^2(2+\ln(3x))}{x(3+x^2)^2} =
\frac{3-3x^2 - 2x^2 \ln(3x)}{x(3+x^2)^2} $">|; 

$key = q/displaystyledyslashdt=-50,x=6,dsslashdt=20.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$ \displaystyle dy/dt = - 50  ,  x=6  ,  ds/dt = 20 .$">|; 

$key = q/displaystylelim_{xrightarrow0}frac{1-cos(2x)}{x^2}=lim_{xrightarrow0}frac{1-cos(box{sen},{2x}}{2x}frac{1}{1+cos(2x)}=4cdot(1)^2frac{1}{1+1}=2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="1414" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\displaystyle \lim_{x \rightarrow 0} \frac{1-\cos(2x)}{x^2} =
\lim_{x \rightarr...
...c{\mbox{sen}   {2x}}{2x}\frac{1}
{1+\cos(2x)} =
4\cdot (1)^2 \frac{1}{1+1} = 2$">|; 

$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="|."$dir".q|img23.png"
 ALT="$f(x)$">|; 

$key = q/a=9;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$a=9$">|; 

$key = q/f'(sqrt{pi});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$f'(\sqrt{\pi})$">|; 

$key = q/displaystylef'(1slash3)=frac{3-3(1slash3)^2-2(1slash3)^2ln(3cdot1slash3)}{1slashh3-0}{1slash3(28slash9)^2}=frac{8slash3}{1slash3(28slash9)^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="550" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\displaystyle f'(1/3) = \frac{3-3(1/3)^2-2(1/3)^2 \ln(3 \cdot 1/3)}
{1/3(3+(1/3)^2)^2} = \frac{3 - 1/3 - 0}{1/3(28/9)^2}=
\frac{8/3}{1/3(28/9)^2} $">|; 

$key = q/displaystylelim_{xrightarrow3^{-}}frac{f(x)-f(3)}{x-3}=lim_{xrightarrow3^{-}}-(x+3)=-(3+3)=-6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle \lim_{x \rightarrow 3^{-}} \frac{f(x)-f(3)}{x-3} =
\lim_{x \rightarrow 3^{-}} -(x+3) = -(3+3)=-6$">|; 

$key = q/displaystylelim_{xrightarrowpminfty}frac{ax^n+3}{3x^5+2}=lim_{xrightarrowpminftyRightarrowleft{array{{l}n=5aslash3=3Rightarrowa=9array{right.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle \lim_{x \rightarrow \pm \infty} \frac{a x^n+3}{3x^5 + 2}
= \lim_{...
...\left\{ \begin{array}{l} n = 5 \ a/3 = 3 \Rightarrow
a = 9 \end{array} \right.$">|; 

$key = q/displaystylef(x)=left{array{{lr}x^2-15,&|x|geq33-x^2,&|x|<3array{right.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle f(x) = \left\{ \begin{array}{lr}
x^2 - 15, &amp; \vert x\vert \geq 3 \\\\
3 - x^2, &amp; \vert x\vert &lt; 3 \end{array} \right. $">|; 

$key = q/displaystylef(x)=|x^2-9|-6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\displaystyle f(x) = \vert x^2 - 9\vert - 6$">|; 

$key = q/x(t);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$x(t)$">|; 

$key = q/displaystylelim_{xrightarrow0}frac{1-cos(2x)}{x^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\displaystyle \lim_{x \rightarrow 0}
\frac{1-\cos(2x)}{x^2}$">|; 

$key = q/y=f(x);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$y = f(x)$">|; 

$key = q/displaystyley-2=f'(1)(x-1)Rightarrowy-2=9(x-1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle y-2 = f'(1)(x-1) \Rightarrow y-2 = 9(x-1)$">|; 

$key = q/displaystylefrac{dy}{dx}=frac{2sqrt{pi}-sqrt{pi}cos(pi)}{2sqrt{pi}+sqrt{pi}cos(p{pi}(-1)}{2sqrt{pi}+sqrt{pi}(-1)}=frac{3sqrt{pi}}{sqrt{pi}}=3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle \frac{dy}{dx} = \frac{ 2 \sqrt{\pi} - \sqrt{\pi} \cos(\pi)}
{2\sq...
...{\pi}(-1)}{2 \sqrt{\pi} + \sqrt{\pi}(-1)} =
\frac{3\sqrt{\pi}}{\sqrt{\pi}} = 3$">|; 

$key = q/displaystylef(x)=(x^2-9)-6=x^2-15;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle f(x) = (x^2-9)-6 = x^2 - 15$">|; 

$key = q/displaystylef(x)=frac{ax^n+3}{3x^5+2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$\displaystyle f(x) = \frac{a x^n + 3}{3x^5 + 2}$">|; 

$key = q/|x|<3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\vert x\vert &lt; 3$">|; 

$key = q/displaystyle(10)(20)=(6)frac{dx}{dt}+8(-50);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle (10) (20) = (6) \frac{dx}{dt} + 8 (-50)$">|; 

$key = q/displaystylefrac{dy}{dx}=e^{x^3+3sqrt{x}}cdotfrac{d}{dx}(x^3+3x^{1slash2});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\displaystyle \frac{dy}{dx} = e^{x^3 + 3\sqrt{x}} \cdot \frac{d}{dx}(x^3 + 3x^{1/2})$">|; 

$key = q/y=3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$y=3$">|; 

$key = q/x=sqrt{pi}Rightarrowy=sqrt{pi};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$x=\sqrt{\pi} \Rightarrow y = \sqrt{\pi}$">|; 

$key = q/f'(3);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$f'(3)$">|; 

$key = q/displaystylef'(1slash3)=8left(frac{9}{28}right)^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\displaystyle f'(1/3) = 8 \left( \frac{9}{28} \right)^2$">|; 

$key = q/f(x)rightarrow3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$f(x) \rightarrow 3$">|; 

$key = q/displaystylesfrac{ds}{dt}=xfrac{dx}{dt}+yfrac{dy}{dt};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle s \frac{ds}{dt} = x \frac{dx}{dt} + y \frac{dy}{dt}$">|; 

$key = q/displaystylex=6,y=8Rightarrows^2=6^2+8^2=36+64=100Rightarrows=10;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle x = 6, y = 8 \Rightarrow s^2 = 6^2 + 8^2 = 36 + 64 = 100
\Rightarrow s = 10$">|; 

$key = q/s^2=x^2+y^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$s^2 = x^2 + y^2$">|; 

$key = q/dxslashdt;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$dx/dt$">|; 

$key = q/f(x)=5x^2-3sqrt[3]{x};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$f(x)=5x^2 - 3
\sqrt[3]{x}$">|; 

1;