# LaTeX2HTML 96.1-f (May 31, 1996)
# Associate images original text with physical files.

$key = q/{}frameboxRightShift{}/;
$cached_env_img{$key} = ' <IMG WIDTH=92 HEIGHT=27 ALIGN=BOTTOM ALT="tex2html_wrap925" SRC="img10.gif"  > '; 
$key = q/{_inline}$cos(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=41 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline949" SRC="img18.gif"  > '; 
$key = q/{_inline}$rightarrowfrac14ln(x-2)-frac14ln(x+2)-left(frac14ln(alpha-2)-frac14ln(alpha+2)right)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=408 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline959" SRC="img21.gif"  > '; 
$key = q/{_inline}$sinh(x)cosh(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=104 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline857" SRC="img4.gif"  > '; 
$key = q/{_inline}$cosh(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=50 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline953" SRC="img20.gif"  > '; 
$key = q/{_inline}$0,(3+sqrt3i)2,(3-sqrt3i)2${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=191 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline1177" SRC="img58.gif"  > '; 
$key = q/{_inline}$pi${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=8 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline1345" SRC="img78.gif"  > '; 
$key = q/{_inline}$sinh(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=48 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline951" SRC="img19.gif"  > '; 
$key = q/{_inline}$xln(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=45 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline967" SRC="img23.gif"  > '; 
$key = q/{}framebox+{}/;
$cached_env_img{$key} = ' <IMG WIDTH=25 HEIGHT=23 ALIGN=BOTTOM ALT="tex2html_wrap927" SRC="img11.gif"  > '; 
$key = q/{_inline}$cos(nx)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=51 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline1089" SRC="img46.gif"  > '; 
$key = q/{_inline}$sqrt2${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=22 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline1075" SRC="img40.gif"  > '; 
$key = q/{_inline}$I!!R${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=13 HEIGHT=11 ALIGN=BOTTOM ALT="tex2html_wrap_inline849" SRC="img1.gif"  > '; 
$key = q/{_inline}$pm${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=10 HEIGHT=20 ALIGN=MIDDLE ALT="tex2html_wrap_inline903" SRC="img15.gif"  > '; 
$key = q/{_inline}$cos(3x)=-3*cos(x)+4*cos(x)^3${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=249 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline1121" SRC="img51.gif"  > '; 
$key = q/{_inline}$partial_1z(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=44 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline1083" SRC="img44.gif"  > '; 
$key = q/{_inline}$sin(nx)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=49 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline1091" SRC="img47.gif"  > '; 
$key = q/{_inline}$sin(3x)=(-1+4cos(x)^2)sin(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=232 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline1119" SRC="img50.gif"  > '; 
$key = q/{_inline}$sqrtx${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=23 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline895" SRC="img12.gif"  > '; 
$key = q/{_inline}$(a,b)=atimesb${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=92 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline1385" SRC="img85.gif"  > '; 
$key = q/{tabular}|l|l|l|l|hlineProgram;SPMamp;Option;SPMamp;Input;SPMamp;OutputhlineRED;SPMamp;RANG;SPMamp;1:matrix;SPMamp;2:pivots,1:redcuedmatrixhlineRED;SPMamp;RED;SPMamp;1:matrix;SPMamp;2:pivots,1:rref-edmatrixhlineRED;SPMamp;DET;SPMamp;1:matrix;SPMamp;3:pivots,2:reducedmatrix,1:determinanthlineRED;SPMamp;INVL;SPMamp;1:matrix;SPMamp;2:pivots,1:inversehlineRED;SPMamp;SYST;SPMamp;2:matrix,1:listofunknowns;SPMamp;4:listunknowns,;SPMamp;;SPMamp;;SPMamp;3:listofprincipalsandauxiliaryunknowns;SPMamp;;SPMamp;;SPMamp;2:listofpivots;SPMamp;;SPMamp;;SPMamp;1:listoftaggedalgebraicshlineRED;SPMamp;SOLGEN;SPMamp;2:matrix,1:listofunknowns;SPMamp;5:pivots,4:listofunknowns,;SPMamp;;SPMamp;;SPMamp;3:listofprincipalandauxiliaryunknowns;SPMamp;;SPMamp;;SPMamp;2:listoftaggedalgebraics,1:resulthline{tabular}/;
$cached_env_img{$key} = ' <IMG WIDTH=751 HEIGHT=245 ALIGN=BOTTOM ALT="tabular250" SRC="img70.gif"  > '; 
$key = q/{_inline}$frac3pmsqrt3i2${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=40 HEIGHT=35 ALIGN=MIDDLE ALT="tex2html_wrap_inline1175" SRC="img56.gif"  > '; 
$key = q/{_inline}$cos${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=19 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline1405" SRC="img88.gif"  > '; 
$key = q/{_inline}$sin${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=17 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap_inline1403" SRC="img87.gif"  > '; 
$key = q/{_inline}$det(A)^-1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=61 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline1161" SRC="img53.gif"  > '; 
$key = q/{_inline}$partial${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=7 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap_inline897" SRC="img13.gif"  > '; 
$key = q/{tabular}|l|l|l|l|l|l|hlineTruedata;SPMamp;Example;SPMamp;User;SPMamp;Example;SPMamp;Internal;SPMamp;ExamplehlineInteger;SPMamp;5;SPMamp;real;SPMamp;5;SPMamp;real;SPMamp;5Float;SPMamp;5.02;SPMamp;real;SPMamp;5.02;SPMamp;real;SPMamp;5Complex;SPMamp;_inline$1+2i$_inline;SPMamp;symbolic;SPMamp;<verb_mark>73<verb_mark>;SPMamp;complex;SPMamp;<verb_mark>74<verb_mark>Complex;SPMamp;(1.1,2.3);SPMamp;complex;SPMamp;<verb_mark>75<verb_mark>;SPMamp;complex;SPMamp;<verb_mark>76<verb_mark>Fractions;SPMamp;_inline$frac23$_inline;SPMamp;symbolic;SPMamp;<verb_mark>77<verb_mark>;SPMamp;symbolic;SPMamp;<verb_mark>78<verb_mark>Irr.quadr.;SPMamp;_inline$1+2sqrt5$_inline;SPMamp;symbolic;SPMamp;<verb_mark>79<verb_mark>;SPMamp;program;SPMamp;<verb_mark>80<verb_mark>Unknowns;SPMamp;_inline$a$_inline,_inline$x$_inline...;SPMamp;variables;SPMamp;<verb_mark>81<verb_mark><verb_mark>82<verb_mark>;SPMamp;list;SPMamp;emvariableSymbolics;SPMamp;_inline$a+x^2$_inline;SPMamp;symbolic;SPMamp;<verb_mark>83<verb_mark>;SPMamp;list;SPMamp;emvariableLists;SPMamp;<verb_mark>84<verb_mark>1_inline$i$_inline<verb_mark>85<verb_mark>;SPMamp;list;SPMamp;<verb_mark>86<verb_mark>;SPMamp;list;SPMamp;<verb_mark>87<verb_mark>Array;SPMamp;<verb_mark>88<verb_mark>;SPMamp;array;SPMamp;<verb_mark>89<verb_mark>;SPMamp;array;SPMamp;<verb_mark>90<verb_mark>Symb.array;SPMamp;<verb_mark>91<verb_mark>;SPMamp;list;SPMamp;<verb_mark>92<verb_mark>;SPMamp;list;SPMamp;<verb_mark>93<verb_mark>hline{tabular}/;
$cached_env_img{$key} = ' <IMG WIDTH=833 HEIGHT=243 ALIGN=BOTTOM ALT="tabular58" SRC="img6.gif"  > '; 
$key = q/{_inline}$I!!!!C${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=11 HEIGHT=11 ALIGN=BOTTOM ALT="tex2html_wrap_inline851" SRC="img2.gif"  > '; 
$key = q/{_inline}$sqrtx^2-1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=59 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline969" SRC="img24.gif"  > '; 
$key = q/{_inline}$sqrtx^3-1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=59 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline1081" SRC="img43.gif"  > '; 
$key = q/{_inline}$1(sin(x)+2)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=97 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline973" SRC="img25.gif"  > '; 
$key = q/{_inline}$sin(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=39 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline947" SRC="img17.gif"  > '; 
$key = q/{_inline}$leftrightarrow${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=14 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline1351" SRC="img79.gif"  > '; 
$key = q/{_inline}$-sin(x)x^2+cos(x)x${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=161 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline975" SRC="img28.gif"  > '; 
$key = q/{}framebox_inline$alpha$_inline{}/;
$cached_env_img{$key} = ' <IMG WIDTH=22 HEIGHT=19 ALIGN=BOTTOM ALT="tex2html_wrap921" SRC="img9.gif"  > '; 
$key = q/{_inline}$rightarrowfrac14ln(x-2)-frac14ln(x+2)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=194 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline961" SRC="img22.gif"  > '; 
$key = q/{_inline}$^-1times${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=27 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline1131" SRC="img52.gif"  > '; 
$key = q/{_inline}$2xsqrt(x^2)3-1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=101 HEIGHT=31 ALIGN=MIDDLE ALT="tex2html_wrap_inline1087" SRC="img45.gif"  > '; 
$key = q/{_inline}$ntimesn${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=38 HEIGHT=16 ALIGN=MIDDLE ALT="tex2html_wrap_inline1017" SRC="img35.gif"  > '; 
$key = q/{_inline}$frac12${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=7 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline1077" SRC="img41.gif"  > '; 
$key = q/{_inline}$sin(x)cos(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=86 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline855" SRC="img3.gif"  > '; 
$key = q/{_inline}$(a,b)times${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=45 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline1383" SRC="img84.gif"  > '; 
$key = q/{_inline}$varepsilon${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=4 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline1359" SRC="img81.gif"  > '; 
$key = q/{_inline}$zrightarrowz(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=63 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline1079" SRC="img42.gif"  > '; 
$key = q/{_inline}$varepsilontimes10${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=41 HEIGHT=20 ALIGN=MIDDLE ALT="tex2html_wrap_inline1357" SRC="img80.gif"  > '; 
$key = q/{tabular}|l|l|l|hlinePrinc.Key;SPMamp;Second.Key;SPMamp;FunctionhlineEVAL;SPMamp;;SPMamp;L2SSIN;SPMamp;Derivative;SPMamp;FDERCOS;SPMamp;Integration;SPMamp;FINTG_inline$sqrt,$_inline;SPMamp;_inline$sqrt,$_inline;SPMamp;SQRT_inline$y^x$_inline;SPMamp;_inline$y^x$_inline;SPMamp;POWER_inline$1x$_inline;SPMamp;_inline$1x$_inline;SPMamp;MAD_inline$pm$_inline;SPMamp;_inline$pm$_inline;SPMamp;CHS7;SPMamp;SOLVE;SPMamp;FROOTS8;SPMamp;PLOT;SPMamp;TSIMP9;SPMamp;ALGEBRA;SPMamp;EXPADivision;SPMamp;Division;SPMamp;DIV14;SPMamp;TIME;SPMamp;tEVAL5;SPMamp;;SPMamp;EXEC6;SPMamp;;SPMamp;COLC*;SPMamp;;SPMamp;MULT1;SPMamp;;SPMamp;clearsflag132;SPMamp;;SPMamp;setsflag133;SPMamp;UNITS;SPMamp;AXL-;SPMamp;-;SPMamp;SUBTSPC;SPMamp;;SPMamp;rref+;SPMamp;+;SPMamp;addhline{tabular}/;
$cached_env_img{$key} = ' <IMG WIDTH=809 HEIGHT=1098 ALIGN=BOTTOM ALT="tabular377" SRC="img91.gif"  > '; 
$key = q/{_inline}$sqrtax^2+bx+c${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=104 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline859" SRC="img5.gif"  > '; 
$key = q/{_inline}$alpha${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=7 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline879" SRC="img8.gif"  > '; 
$key = q/{_inline}$rightarrow${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=14 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline913" SRC="img16.gif"  > '; 
$key = q/{_inline}$v_3(0,3,1)inI!!R^3${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=111 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline1251" SRC="img69.gif"  > '; 
$key = q/{_inline}$int${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=8 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline899" SRC="img14.gif"  > '; 

1;

