Difference between revisions of "File:Tet10bxr.jpg"

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Line 1: Line 1:
−
$y=\mathrm{tet}_b(x)$ versus $x$ for various values of $b$.
 +
[[Explicit plot]] of [[tetration]] for real values of base $b\!>\!1$.
   
  +
$y\!=\! \mathrm{tet}_b(x)$ versus $x$ for various $b$
−
Generators:
  
−
[[efjh.cin]]
  
−
[[Tet10bxq.cc]]
  
−
[[Tet10bxr.tex]]
  
   
  +
==[[C++]] generator of curves==
  +
Files
  +
[[ado.cin]],
  +
[[fit1.cin]],
  +
[[efjh.cin]],
  +
[[f2048ten.inc]],
  +
[[f4ten.cin]]
  +
should be loaded in order to compile the code below
  +
<poem><nomathjax><nowiki>
  +
#include <math.h>
  +
#include <stdio.h>
  +
#include <stdlib.h>
  +
#define DB double
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
//using namespace std;
  +
#include <complex>
  +
typedef std::complex<double> z_type;
  +
#define Re(x) x.real()
  +
#define Im(x) x.imag()
  +
#define I z_type(0.,1.)
  +
//b=10
  +
#include "f4ten.cin"
  +
#include "fit1.cin"
  +
void ado(FILE *O, int X, int Y)
  +
{ fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
  +
fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
  +
fprintf(O,"/M {moveto} bind def\n");
  +
fprintf(O,"/L {lineto} bind def\n");
  +
fprintf(O,"/S {stroke} bind def\n");
  +
fprintf(O,"/s {show newpath} bind def\n");
  +
fprintf(O,"/C {closepath} bind def\n");
  +
fprintf(O,"/F {fill} bind def\n");
  +
fprintf(O,"/o {.1 0 360 arc C S} bind def\n");
  +
fprintf(O,"/times-Roman findfont 20 scalefont setfont\n");
  +
fprintf(O,"/W {setlinewidth} bind def\n");
  +
fprintf(O,"/RGB {setrgbcolor} bind def\n");}
  +
//#include "ado.cin"
  +
#define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
  +
#define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
  +
#define o(x,y) fprintf(o,"%6.4f %6.4f o\n",0.+x,0.+y);
  +
int main(){ int j,k,m,n; DB p,q,t1,t3,u,v,w,x,y; z_type z,c,d;
  +
FILE *o;o=fopen("tet10bx.eps","w");ado(o,134,124);
  +
fprintf(o,"22 22 translate\n 10 10 scale\n");
  +
fprintf(o,"2 setlinecap\n");
  +
for(m=-2;m<12;m++){if(m!=0){M(m,-2)L(m,10)}}
  +
for(n= -2;n<11;n++){if(n!=0){M(-2,n)L(11,n)}} fprintf(o,".006 W 0 0 0 RGB S\n");
  +
M(-2,0)L(11.1,0) M(0, -2)L(0,10.1) fprintf(o,".03 W 0 0 0 RGB S\n");
  +
M(0,M_E)L(11.,M_E) fprintf(o,".006 W 0 0 0 RGB S\n");
  +
fprintf(o,"1 setlinejoin 1 setlinecap\n");
  +
//DO(m,400){x=-1.99+.008*m;y=Re(FIT1(log(10.),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W .5 0 .5 RGB S\n");
  +
DO(m,400){x=-1.80+.02*m; y=Re(FIT1(log(2.),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W .5 0 .5 RGB S\n");
  +
DO(m,400){x=-1.78+.02*m; y=Re(FIT1(log(1.9),x)); if(y>10.33) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
  +
DO(m,400){x=-1.77+.02*m; y=Re(FIT1(log(1.8),x)); if(y>10.33) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
  +
DO(m,400){x=-1.74+.02*m; y=Re(FIT1(log(1.7),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
  +
DO(m,400){x=-1.72+.03*m; y=Re(FIT1(log(1.6),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
  +
DO(m,400){x=-1.68+.04*m; y=Re(FIT1(log(1.5),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
  +
DO(m,400){x=-1.64+.04*m; y=Re(FIT1(log(1.4),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
  +
DO(m,400){x=-1.58+.04*m; y=Re(FIT1(log(1.3),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
  +
DO(m,400){x=-1.52+.04*m; y=Re(FIT1(log(1.2),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
  +
DO(m,400){x=-1.42+.04*m; y=Re(FIT1(log(1.1),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
  +
//
  +
DO(m,400){x=-1.65+.04*m; y=Re(FIT1(1./M_E,x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W 0 0 .7 RGB S\n");
  +
DO(m,400){x=-1.64+.04*m; y=Re(FIT1(log(sqrt(2.)),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W .8 0 0 RGB S\n");
  +
DO(m,400){x=-1.873+.01*m; y=Re(FIT1(1.,x)); if(y>11) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 0 RGB S\n");
  +
//
  +
DO(m,401){x=-1.987+.01*m;y=Re(F4TEN(x));if(m==0)M(x,y)else L(x,y)}fprintf(o,".02 W .5 0 .5 RGB S\n");
  +
//DO(m,39){x=-1.89+.098*m; y=Re(FSEXP(x));if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
  +
//DO(m,48){x=-1.82+.0973*m; y=Re(F2(x)); if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
  +
//DO(m,126){x=-1.72+.1*m; y=Re(F15(x)); if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
  +
//DO(m,130){x=-1.65+.1*m; y=Re(E1ETF(x)); if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
  +
//DO(m,130){x=-1.64+.1*m; y=Re(f21E(x)); if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
  +
M(-1.998,-2)L(-1.992,-.01)L(-1,0)L(-.01,.01)L(0,1)L(.012,10.1) fprintf(o,".02 W .4 0 .8 RGB S\n");
  +
M(-1.01,-2)L(-1,0)L(-.99,.99)L(0,1)L(10.97,1.01) fprintf(o,".02 W .2 .4 0 RGB S\n");
  +
fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
  +
system("epstopdf tet10bx.eps");
  +
system( "open tet10bx.pdf"); //mac
  +
// system( "xpdf tet10bx.pdf"); // linux
  +
getchar(); system("killall Preview");// mac
  +
}
  +
</nowiki></nomathjax></poem>
   
  +
==[[Latex]] generator of curves==
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{geometry} % See geometry.pdf
  +
\geometry{letterpaper} % ... or a4paper or a5paper or ... ??
  +
\usepackage{graphicx}
  +
\usepackage{amssymb}
  +
\usepackage{hyperref}
  +
\usepackage{rotating}
  +
\usepackage[utf8x]{inputenc}
  +
\usepackage[english,russian]{babel}
  +
\usepackage{color}
  +
\definecolor{red}{rgb}{1,0.1,0.1}
  +
\definecolor{black}{rgb}{0,0,0}
  +
\definecolor{white}{rgb}{1,1,1}
  +
\definecolor{yellow}{rgb}{1,.93,0}
  +
\definecolor{bluedark}{rgb}{0,0,.87}
  +
\paperwidth 528pt
  +
\paperheight 488pt
  +
\topmargin -102pt
  +
\oddsidemargin -78pt
  +
\textwidth 610pt
  +
\textheight 570pt
  +
  +
\newcommand \sx {\scalebox}
  +
\newcommand \ing {\includegraphics}
  +
\newcommand \tet {\mathrm{tet}}
  +
\newcommand \pen {\mathrm{pen}}
  +
\newcommand \bC {\mathbb C}
  +
\newcommand \fac {\mathrm {Factorial}}
  +
\newcommand \rme {\mathrm e}
  +
\newcommand \rmi {\mathrm i}
  +
\newcommand \ds {\displaystyle}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
  +
\begin{document}
  +
\parindent 0pt
  +
\sx{4}
  +
{\normalsize
  +
\begin{picture}(155,122)
  +
\put(0,0){\ing{tet10bx}}
  +
%\put(-2,125){\sx{.7}{$y\!=\!{\rm tet}_{b}(x)$ ~as solution of~ $F(z\!+\!1)=\exp_b(F(z))$ ~,~ $F(0)\!=\!1$}}
  +
%\put( 0,125){\sx{.55}{$y\!=\!F(x)$ ~as solution of~ $F(z\!+\!1)\!=\!\exp_b(F(z))$ ,~ $F(0)\!=\!1$}}
  +
\put( 17,120){\sx{.6}{$y$}}
  +
\put( 17,100){\sx{.6}{$8$}}
  +
\put( 17,80){\sx{.6}{$6$}}
  +
\put( 17,60){\sx{.6}{$4$}}
  +
\put( 18,48){\sx{.6}{e}}
  +
\put( 17,40){\sx{.6}{$2$}}
  +
\put( 17,20){\sx{.6}{$0$}}
  +
\put( 20.4,16){\sx{.6}{$0$}}
  +
\put( 40.4,16){\sx{.6}{$2$}}
  +
\put( 60.4,16){\sx{.6}{$4$}}
  +
\put( 80.4,16){\sx{.6}{$6$}}
  +
\put(100.4,16){\sx{.6}{$8$}}
  +
\put(119,16){\sx{.6}{$10$}}
  +
\put(128.6,16.2){\sx{.6}{$x$}}
  +
%\put(2,90){\sx{.9}{$y\!=\!e\!\big(F_{1}(x\!+\!\rmi o)\big)$}}
  +
%\put(183,105){\sx{1.}{$y\!=\!F_{3}(x)$}}
  +
%\put(193,52){\sx{1.}{$y\!=\!\rme$}}
  +
\put(26.6,86){\sx{.5}{\rot{90} $b\!\rightarrow\!\infty$ \ero } }
  +
\put(31,106){\sx{.5}{\rot{88} $b\!=\!10$ \ero } }
  +
%\put(39.2,106){\sx{.5}{\rot{86} $b\!=\! 3$ \ero } }
  +
\put(42,87){\sx{.5}{\rot{87} $b\!=\! \rme$ \ero } }
  +
\put(48.4,106){\sx{.5}{\rot{86} $b\!=\!2$ \ero } }
  +
\put(53.3,106){\sx{.45}{\rot{85} $b\!=\!1.9$ \ero } }
  +
\put(60.3,106){\sx{.45}{\rot{85} $b\!=\!1.8$ \ero } }
  +
\put(68.4,106){\sx{.45}{\rot{84} $b\!=\!1.7$ \ero } }
  +
\put(83,106){\sx{.45}{\rot{83} $b\!=\!1.6$ \ero } }
  +
\put(128,106){\sx{.47}{\rot{80} $b\!=\!1.5$ \ero } }
  +
%\put(55,88){\sx{1.3}{$y\!=\!\tet_b(x)$ } }
  +
%\put(124,106){\sx{.6}{$b\!=\!1.5$}}
  +
\put(109,46){\sx{.4}{\rot{2}$b\!=\!\exp(1/\rme)$\ero}}
  +
\put(120,41.8){\sx{.34}{$b\!=\!\sqrt{2}$}}
  +
\put(120,38){\sx{.36}{$b\!=\!1.4$}}
  +
\put(120,33.6){\sx{.36}{$b\!=\!1.2$}}
  +
%\put(115,29.6){\sx{.36}{$b\!=\!1.1$}}
  +
\put(123,29){\sx{.36}{$b\!\rightarrow\!1$}}
  +
\end{picture}}
  +
\end{document}
  +
</nowiki></nomathjax></poem>
  +
  +
  +
[[Category:Book]]
  +
[[Category:BookPlot]]
  +
[[Category:Esplicit plot]]
  +
[[Category:C++]]
  +
[[Category:Iterate]]
  +
[[Category:Latex]]
 
[[Category:Mathematical functions]]
  
[[Category:Mathematical functions]]
 
[[Category:Superfunctions]]
  
[[Category:Superfunctions]]

Latest revision as of 08:53, 1 December 2018

Explicit plot of tetration for real values of base $b\!>\!1$.

$y\!=\! \mathrm{tet}_b(x)$ versus $x$ for various $b$

C++ generator of curves

Files ado.cin, fit1.cin, efjh.cin, f2048ten.inc, f4ten.cin should be loaded in order to compile the code below


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
//using namespace std;
#include <complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
//b=10
#include "f4ten.cin"
#include "fit1.cin"
void ado(FILE *O, int X, int Y)
{ fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
       fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
       fprintf(O,"/M {moveto} bind def\n");
       fprintf(O,"/L {lineto} bind def\n");
       fprintf(O,"/S {stroke} bind def\n");
       fprintf(O,"/s {show newpath} bind def\n");
       fprintf(O,"/C {closepath} bind def\n");
       fprintf(O,"/F {fill} bind def\n");
       fprintf(O,"/o {.1 0 360 arc C S} bind def\n");
       fprintf(O,"/times-Roman findfont 20 scalefont setfont\n");
       fprintf(O,"/W {setlinewidth} bind def\n");
       fprintf(O,"/RGB {setrgbcolor} bind def\n");}
 //#include "ado.cin"
#define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
#define o(x,y) fprintf(o,"%6.4f %6.4f o\n",0.+x,0.+y);
int main(){ int j,k,m,n; DB p,q,t1,t3,u,v,w,x,y; z_type z,c,d;
FILE *o;o=fopen("tet10bx.eps","w");ado(o,134,124);
fprintf(o,"22 22 translate\n 10 10 scale\n");
fprintf(o,"2 setlinecap\n");
for(m=-2;m<12;m++){if(m!=0){M(m,-2)L(m,10)}}
for(n= -2;n<11;n++){if(n!=0){M(-2,n)L(11,n)}} fprintf(o,".006 W 0 0 0 RGB S\n");
M(-2,0)L(11.1,0) M(0, -2)L(0,10.1) fprintf(o,".03 W 0 0 0 RGB S\n");
M(0,M_E)L(11.,M_E) fprintf(o,".006 W 0 0 0 RGB S\n");
fprintf(o,"1 setlinejoin 1 setlinecap\n");
//DO(m,400){x=-1.99+.008*m;y=Re(FIT1(log(10.),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W .5 0 .5 RGB S\n");
DO(m,400){x=-1.80+.02*m; y=Re(FIT1(log(2.),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W .5 0 .5 RGB S\n");
DO(m,400){x=-1.78+.02*m; y=Re(FIT1(log(1.9),x)); if(y>10.33) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.77+.02*m; y=Re(FIT1(log(1.8),x)); if(y>10.33) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.74+.02*m; y=Re(FIT1(log(1.7),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.72+.03*m; y=Re(FIT1(log(1.6),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.68+.04*m; y=Re(FIT1(log(1.5),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.64+.04*m; y=Re(FIT1(log(1.4),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.58+.04*m; y=Re(FIT1(log(1.3),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.52+.04*m; y=Re(FIT1(log(1.2),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.42+.04*m; y=Re(FIT1(log(1.1),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
//
DO(m,400){x=-1.65+.04*m; y=Re(FIT1(1./M_E,x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W 0 0 .7 RGB S\n");
DO(m,400){x=-1.64+.04*m; y=Re(FIT1(log(sqrt(2.)),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W .8 0 0 RGB S\n");
DO(m,400){x=-1.873+.01*m; y=Re(FIT1(1.,x)); if(y>11) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 0 RGB S\n");
//
DO(m,401){x=-1.987+.01*m;y=Re(F4TEN(x));if(m==0)M(x,y)else L(x,y)}fprintf(o,".02 W .5 0 .5 RGB S\n");
//DO(m,39){x=-1.89+.098*m; y=Re(FSEXP(x));if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
//DO(m,48){x=-1.82+.0973*m; y=Re(F2(x)); if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
//DO(m,126){x=-1.72+.1*m; y=Re(F15(x)); if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
//DO(m,130){x=-1.65+.1*m; y=Re(E1ETF(x)); if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
//DO(m,130){x=-1.64+.1*m; y=Re(f21E(x)); if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
M(-1.998,-2)L(-1.992,-.01)L(-1,0)L(-.01,.01)L(0,1)L(.012,10.1) fprintf(o,".02 W .4 0 .8 RGB S\n");
M(-1.01,-2)L(-1,0)L(-.99,.99)L(0,1)L(10.97,1.01) fprintf(o,".02 W .2 .4 0 RGB S\n");
fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
       system("epstopdf tet10bx.eps");
       system( "open tet10bx.pdf"); //mac
// system( "xpdf tet10bx.pdf"); // linux
getchar(); system("killall Preview");// mac
}

Latex generator of curves


\documentclass[12pt]{article}
\usepackage{geometry} % See geometry.pdf
\geometry{letterpaper} % ... or a4paper or a5paper or ... ??
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{hyperref}
\usepackage{rotating}
\usepackage[utf8x]{inputenc}
\usepackage[english,russian]{babel}
\usepackage{color}
\definecolor{red}{rgb}{1,0.1,0.1}
\definecolor{black}{rgb}{0,0,0}
\definecolor{white}{rgb}{1,1,1}
\definecolor{yellow}{rgb}{1,.93,0}
\definecolor{bluedark}{rgb}{0,0,.87}
\paperwidth 528pt
\paperheight 488pt
\topmargin -102pt
\oddsidemargin -78pt
\textwidth 610pt
\textheight 570pt

\newcommand \sx {\scalebox}
\newcommand \ing {\includegraphics}
\newcommand \tet {\mathrm{tet}}
\newcommand \pen {\mathrm{pen}}
\newcommand \bC {\mathbb C}
\newcommand \fac {\mathrm {Factorial}}
\newcommand \rme {\mathrm e}
\newcommand \rmi {\mathrm i}
\newcommand \ds {\displaystyle}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}

\begin{document}
\parindent 0pt
\sx{4}
{\normalsize
\begin{picture}(155,122)
\put(0,0){\ing{tet10bx}}
%\put(-2,125){\sx{.7}{$y\!=\!{\rm tet}_{b}(x)$ ~as solution of~ $F(z\!+\!1)=\exp_b(F(z))$ ~,~ $F(0)\!=\!1$}}
%\put( 0,125){\sx{.55}{$y\!=\!F(x)$ ~as solution of~ $F(z\!+\!1)\!=\!\exp_b(F(z))$ ,~ $F(0)\!=\!1$}}
\put( 17,120){\sx{.6}{$y$}}
\put( 17,100){\sx{.6}{$8$}}
\put( 17,80){\sx{.6}{$6$}}
\put( 17,60){\sx{.6}{$4$}}
\put( 18,48){\sx{.6}{e}}
\put( 17,40){\sx{.6}{$2$}}
\put( 17,20){\sx{.6}{$0$}}
\put( 20.4,16){\sx{.6}{$0$}}
\put( 40.4,16){\sx{.6}{$2$}}
\put( 60.4,16){\sx{.6}{$4$}}
\put( 80.4,16){\sx{.6}{$6$}}
\put(100.4,16){\sx{.6}{$8$}}
\put(119,16){\sx{.6}{$10$}}
\put(128.6,16.2){\sx{.6}{$x$}}
%\put(2,90){\sx{.9}{$y\!=\!e\!\big(F_{1}(x\!+\!\rmi o)\big)$}}
%\put(183,105){\sx{1.}{$y\!=\!F_{3}(x)$}}
%\put(193,52){\sx{1.}{$y\!=\!\rme$}}
\put(26.6,86){\sx{.5}{\rot{90} $b\!\rightarrow\!\infty$ \ero } }
\put(31,106){\sx{.5}{\rot{88} $b\!=\!10$ \ero } }
%\put(39.2,106){\sx{.5}{\rot{86} $b\!=\! 3$ \ero } }
\put(42,87){\sx{.5}{\rot{87} $b\!=\! \rme$ \ero } }
\put(48.4,106){\sx{.5}{\rot{86} $b\!=\!2$ \ero } }
\put(53.3,106){\sx{.45}{\rot{85} $b\!=\!1.9$ \ero } }
\put(60.3,106){\sx{.45}{\rot{85} $b\!=\!1.8$ \ero } }
\put(68.4,106){\sx{.45}{\rot{84} $b\!=\!1.7$ \ero } }
\put(83,106){\sx{.45}{\rot{83} $b\!=\!1.6$ \ero } }
\put(128,106){\sx{.47}{\rot{80} $b\!=\!1.5$ \ero } }
%\put(55,88){\sx{1.3}{$y\!=\!\tet_b(x)$ } }
%\put(124,106){\sx{.6}{$b\!=\!1.5$}}
\put(109,46){\sx{.4}{\rot{2}$b\!=\!\exp(1/\rme)$\ero}}
\put(120,41.8){\sx{.34}{$b\!=\!\sqrt{2}$}}
\put(120,38){\sx{.36}{$b\!=\!1.4$}}
\put(120,33.6){\sx{.36}{$b\!=\!1.2$}}
%\put(115,29.6){\sx{.36}{$b\!=\!1.1$}}
\put(123,29){\sx{.36}{$b\!\rightarrow\!1$}}
\end{picture}}
\end{document}

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