[Tex/LaTex] Plotting sin(1/x) associated functions

pstricks

I need to plot x, -x, x^2, -x^2, sin(1/x), x*sin(1/x), x^2*sin(1/x) and sin(1/x). But the functions containing sin(1/x) looks somehow bad. How can I fix it. I also do not know how to label the graphs (writing y=sin(1/x) next to the curve y=sin(1/x).

\documentclass{article}
\usepackage{pst-func}
\begin{document}
\begin{pspicture}*(-5,-2)(5,2)
\SpecialCoor % For label positionning
\psaxes[labels=y,Dx=\pstPI2]{->}(0,0)(-5,-2)(5,2)
\uput[-90](!PI 0){$\pi$} \uput[-90](!PI neg 0){$-\pi$} 5 \uput[-90](!PI 2 div 0){$\frac{\pi}2$}
\uput[-90](!PI 2 div neg 0){$-\frac{\pi}2$}
\psplot[linewidth=1.5pt,linecolor=blue,algebraic]{-5}{5}{sin(1/x)}
\psplot[linewidth=1.5pt,linecolor=red,algebraic]{-5}{5}{x*sin(1/x)}
\psplot[linewidth=1.5pt,linecolor=green,algebraic]{-5}{5}{x^2*sin(1/x)}
\psplot[algebraic,linestyle=dashed]{-5}{5}{x}
\psplot[algebraic,linestyle=dashed]{-5}{5}{-x}
\psplot[algebraic,linestyle=dashed]{-5}{5}{x^2}
\psplot[algebraic,linestyle=dashed]{-5}{5}{-x^2}
\end{pspicture}
\end{document}


I do not think that you get a better result with the current tools. The following uses always the same units for all functions:

\documentclass[pstricks, margin=5pt]{standalone}
\begin{document}

\def\xLeft{-0.5} \def\xRight{0.5}

\psset{xunit=8,yunit=2}
\begin{pspicture}(\xLeft,-1.2)(0.55,1.3)
labelFontSize=\scriptstyle,Dy=0.5]{->}(0,0)(\xLeft,-1.1)(\xRight,1.2)
\psset{algebraic,linewidth=0.5\pslinewidth}
\psplot[linestyle=dashed]{\xLeft}{\xRight}{x}
\psplot[linestyle=dashed]{\xLeft}{\xRight}{-x}
\psplot[linestyle=dashed]{\xLeft}{\xRight}{x^2}
\psplot[linestyle=dashed]{\xLeft}{\xRight}{-x^2}
%
\psplot[linecolor=blue,plotpoints=500]{\xLeft}{-0.07}{sin(1/x)}
\psplot[linecolor=blue,VarStep,VarStepEpsilon=1.e-8]{-0.07}{-0.001}{sin(1/x)}
\psplot[linecolor=blue,VarStep,VarStepEpsilon=1.e-8]{0.001}{0.07}{sin(1/x)}
\psplot[linecolor=blue,plotpoints=500]{0.07}{\xRight}{sin(1/x)}
%
\psplot[linecolor=red,VarStep,VarStepEpsilon=1.e-9]{\xLeft}{\xRight}{x*sin(1/x)}
%
\psplot[linecolor=green,VarStep,VarStepEpsilon=1.e-9]{\xLeft}{\xRight}{x^2*sin(1/x)}
\end{pspicture}
\end{document}


If you want it similar to what Spivak had, then use different units for the different curves (from the mathematical view it is wrong):

\documentclass[pstricks, margin=5pt]{standalone}
\usepackage{pst-plot}
\begin{document}
\def\xLeft{-0.5} \def\xRight{0.5}

\psset{xunit=8,yunit=2}
\begin{pspicture}(\xLeft,-1.2)(0.55,1.3)
labelFontSize=\scriptstyle,Dy=0.5]{->}(0,0)(\xLeft,-1.1)(\xRight,1.2)
\psset{algebraic,linewidth=0.5\pslinewidth}
%
\psplot[linecolor=blue!50,VarStep,VarStepEpsilon=1.e-8]{\xLeft}{-0.01}{sin(1/x)}
\psplot[linecolor=blue!50,VarStep,VarStepEpsilon=1.e-8]{0.01}{\xRight}{sin(1/x)}
%
\psplot[yunit=3,linecolor=red,VarStep,VarStepEpsilon=1.e-9]{\xLeft}{\xRight}{x*sin(1/x)}
\psplot[yunit=3,linestyle=dashed]{\xLeft}{\xRight}{x}
\psplot[yunit=3,linestyle=dashed]{\xLeft}{\xRight}{-x}
%
\psplot[yunit=8,linecolor=green,VarStep,VarStepEpsilon=1.e-9]{\xLeft}{\xRight}{x^2*sin(1/x)}
%
\psplot[yunit=8,linestyle=dashed]{\xLeft}{\xRight}{x^2}
\psplot[yunit=8,linestyle=dashed]{\xLeft}{\xRight}{-x^2}
\end{pspicture}
\end{document}