# LaTeX2HTML 2022 (Released January 1, 2022)
# Associate images original text with physical files.


$key = q/displaystylesqrt{{1+(frac{b}{a})^2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.94ex; vertical-align: 174.59ex; " SRC="|."$dir".q|img12.png"
 ALT="$\displaystyle \sqrt{{1 + (\frac{b}{a})^2}}$">|; 

$key = q/displaystylesqrt{{2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.67ex; vertical-align: 173.37ex; " SRC="|."$dir".q|img13.png"
 ALT="$\displaystyle \sqrt{{2}}$">|; 

$key = q/displaystylesqrt{{a^2+b^2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.38ex; vertical-align: 176.44ex; " SRC="|."$dir".q|img2.png"
 ALT="$\displaystyle \sqrt{{a^2 + b^2}}$">|; 

$key = q/displaystyle{frac{{(1+sqrt{2})a}}{{b}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.29ex; vertical-align: 171.34ex; " SRC="|."$dir".q|img17.png"
 ALT="$\displaystyle {\frac{{(1+ \sqrt{2})a}}{{b}}}$">|; 

$key = q/displaystyle{frac{{0.457:(frac{Deltay}{d})^2}}{{frac{Deltax}{d}}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.97ex; vertical-align: 171.83ex; " SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle {\frac{{0.457\:(\frac{\Delta y}{d})^2}}{{\frac{\Delta x}{d}}}}$">|; 

$key = q/displaystyle{frac{{0.457:b^2}}{{a}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.15ex; vertical-align: 171.48ex; " SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle {\frac{{0.457\: b^2}}{{a}}}$">|; 

$key = q/displaystyle{frac{{1+1}}{{frac{b}{a}}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.38ex; vertical-align: 174.26ex; " SRC="|."$dir".q|img14.png"
 ALT="$\displaystyle {\frac{{1+1}}{{\frac{b}{a}}}}$">|; 

$key = q/displaystyle{frac{{1+sqrt{2}}}{{frac{b}{a}}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.76ex; vertical-align: 171.96ex; " SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle {\frac{{1+ \sqrt{2}}}{{\frac{b}{a}}}}$">|; 

$key = q/displaystyle{frac{{1pmsqrt{1+(frac{b}{a})^2}}}{{frac{b}{a}}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.83ex; vertical-align: 168.81ex; " SRC="|."$dir".q|img10.png"
 ALT="$\displaystyle {\frac{{1 \pm \sqrt{1 + (\frac{b}{a})^2}}}{{\frac{b}{a}}}}$">|; 

$key = q/displaystyle{frac{{1}}{{n^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.83ex; vertical-align: 172.81ex; " SRC="|."$dir".q|img6.png"
 ALT="$\displaystyle {\frac{{1}}{{n^2}}}$">|; 

$key = q/displaystyle{frac{{2ab}}{{n}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.18ex; vertical-align: 172.53ex; " SRC="|."$dir".q|img5.png"
 ALT="$\displaystyle {\frac{{2ab}}{{n}}}$">|; 

$key = q/displaystyle{frac{{2a}}{{b}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: 171.90ex; " SRC="|."$dir".q|img15.png"
 ALT="$\displaystyle {\frac{{2a}}{{b}}}$">|; 

$key = q/displaystyle{frac{{2n}}{{(n^2-1)}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.83ex; vertical-align: 172.23ex; " SRC="|."$dir".q|img8.png"
 ALT="$\displaystyle {\frac{{2n}}{{(n^2
-1)}}}$">|; 

$key = q/displaystyle{frac{{2pmsqrt{4+4(frac{b}{a})^2}}}{{frac{2b}{a}}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.32ex; vertical-align: 171.40ex; " SRC="|."$dir".q|img9.png"
 ALT="$\displaystyle {\frac{{2 \pm \sqrt{4 + 4(\frac{b}{a})^2}}}{{\frac{2b}{a}}}}$">|; 

$key = q/displaystyle{frac{{Deltax}}{{d}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.18ex; vertical-align: 172.53ex; " SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle {\frac{{\Delta x}}{{d}}}$">|; 

$key = q/displaystyle{frac{{b^2*(3+sqrt{2})}}{{a*4*(1+sqrt{2})}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.55ex; vertical-align: 172.32ex; " SRC="|."$dir".q|img21.png"
 ALT="$\displaystyle {\frac{{b^2 * (3 + \sqrt{2})}}{{a*4*(1 + \sqrt{2})}}}$">|; 

$key = q/displaystyle{frac{{b^2}}{{(1+sqrt{2})a}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.32ex; vertical-align: 171.48ex; " SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle {\frac{{b^2}}{{(1+ \sqrt{2})a}}}$">|; 

$key = q/displaystyle{frac{{b^2}}{{2a}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.01ex; vertical-align: 171.69ex; " SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle {\frac{{b^2}}{{2a}}}$">|; 

$key = q/displaystyle{frac{{b^2}}{{n^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.83ex; vertical-align: 172.81ex; " SRC="|."$dir".q|img4.png"
 ALT="$\displaystyle {\frac{{b^2}}{{n^2}}}$">|; 

$key = q/displaystyle{frac{{b}}{{a}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.76ex; vertical-align: 172.95ex; " SRC="|."$dir".q|img7.png"
 ALT="$\displaystyle {\frac{{b}}{{a}}}$">|; 

$key = q/displaystyle{frac{{b}}{{n}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.87ex; vertical-align: 174.77ex; " SRC="|."$dir".q|img3.png"
 ALT="$\displaystyle {\frac{{b}}{{n}}}$">|; 

$key = q/displaystyle{frac{{c_l+c_u}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.18ex; vertical-align: 172.53ex; " SRC="|."$dir".q|img20.png"
 ALT="$\displaystyle {\frac{{c_l+c_u}}{{2}}}$">|; 

$key = q/sqrt{{a^2+b^2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 196.25ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1.png"
 ALT="$\sqrt{{a^2 + b^2}}$">|; 

$key = q/{frac{{Deltax}}{{d}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.57ex; vertical-align: 171.93ex; " SRC="|."$dir".q|img25.png"
 ALT="${\frac{{\Delta x}}{{d}}}$">|; 

$key = q/{frac{{b}}{{a}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.83ex; vertical-align: 170.60ex; " SRC="|."$dir".q|img11.png"
 ALT="${\frac{{b}}{{a}}}$">|; 

1;

