\input preamble.tex \Defdim(\k,-0.7) \newdimen\a \newdimen\b \newdimen\x \newdimen\y \def\dsp{\displaystyle} % ------------------------------------------------------------------------- \begin{document} \unitlength1.3cm \begin{center} {\huge \bf{Curve Family I}} \bigskip \begin{lapdf}(14,14)(-7,-7) \Lingrid(10)(1,3)(-7,7)(-7,7) \Rect(-7,-7,14,14) \Setclip \def\FamilyI(#1){\Polynom(-7,+7)(0.1,#1,0,#1) \Stroke} \Whiledim{\k<0.8}{\Stepcol(0,23,2) \FamilyI(\Np\k) \Dadd(\k,0.1)} \Setwidth(0.01) \Black \Dash(1) \Polynom(-7,+7)(-0.05,0,-0.15,0) \Stroke \Dash(0) \Point(1)(+4.67,-5.78) \Point(1)(+4.00,-3.80) \Point(1)(+3.33,-2.35) \Point(1)(+2.67,-1.35) \Point(1)(+2.00,-0.70) \Point(1)(+1.33,-0.32) \Point(1)(+0.67,-0.11) \Point(1)(+0.00,+0.00) \Point(1)(-0.67,+0.11) \Point(1)(-1.33,+0.32) \Point(1)(-2.00,+0.70) \Point(1)(-2.67,+1.35) \Point(1)(-3.33,+2.35) \Point(1)(-4.00,+3.80) \Point(1)(-4.67,+5.78) \Text(-5.8,5,rb){$k=7$} \Text(5.8,-5,lt){$k=-7$} \Text(-4.6,6.2,lb){$f_{e}(x)=-\dsp\frac{1}{20}(x^3+3x)$} \end{lapdf} $f_{k}(x)=\dsp\frac{1}{10}(x^3+kx^2+k)$ \qquad $k = -7 \dots +7$ \newpage {\huge \bf{Curve Family II}} \bigskip \begin{lapdf}(14,14)(-7,-7) \Lingrid(10)(1,3)(-7,7)(-7,7) \Rect(-7,-7,14,14) \Setclip \def\FamilyII(#1){\Polynom(-7,+7)(0.1,#1,0.1,0) \Stroke} \Whiledim{\k<0.8}{\Stepcol(0,23,2) \FamilyII(\Np\k) \Dadd(\k,0.1)} \Setwidth(0.01) \Black \Dash(1) \Polynom(-7,+7)(-0.05,0,0.05,0) \Stroke \Dash(0) \Point(1)(+4.59,-4.62) \Point(1)(+3.91,-2.80) \Point(1)(+3.23,-1.52) \Point(1)(+2.54,-0.69) \Point(1)(+1.82,-0.21) \Point(1)(+1.00,+0.00) \Point(1)(+0.00,+0.00) \Point(1)(-1.00,+0.00) \Point(1)(-1.82,+0.21) \Point(1)(-2.54,+0.69) \Point(1)(-3.23,+1.52) \Point(1)(-3.91,+2.80) \Point(1)(-4.59,+4.62) \Text(-5.6,4.1,rb){$k=7$} \Text(5.6,-4.1,lt){$k=-7$} \Text(-4.9,6.2,lb){$f_{e}(x)=-\dsp\frac{1}{20}(x^3-x)$} \end{lapdf} $f_{k}(x)=\dsp\frac{1}{10}(x^3+kx^2+x)$ \qquad $k = -7 \dots +7$ \newpage {\huge \bf{Curve Family III}} \bigskip \begin{lapdf}(13,11)(-5,-3) \Lingrid(10)(1,3)(-5,8)(-3,8) \Rect(-5,-3,13,11) \Setclip \def\Fx(#1,#2){\Dset(\x,#1) \y=2\k \Sub(\y,\x) \Exp(\Np\y,#2) \Add(#2,\x) \y=3\k \Sub(#2,\y)} \Dset(\k,-1) \Whiledim{\k<3.5}{ \a=\k \Dsub(\a,3.25) \b=\k \Dadd(\b,8) \Stepcol(0,23,2) \Fplot(96)(\Np\a,\Np\b) \Stroke \Dadd(\k,0.5)} \Setwidth(0.01) \Black \Dash(1) \Polynom(-4,+7)(0,0,-0.5,1) \Stroke \Dash(0) \Point(1)(-2.0,+2.0) \Point(1)(-1.0,+1.5) \Point(1)(+0.0,+1.0) \Point(1)(+1.0,+0.5) \Point(1)(+2.0,+0.0) \Point(1)(+3.0,-0.5) \Point(1)(+4.0,-1.0) \Point(1)(+5.0,-1.5) \Point(1)(+6.0,-2.0) \Text(-4.7,7.7,lt){$k=-1$} \Text(+2.9,7.7,lt){$k=+3$} \Text(-4.9,2.1,lb){$y_e=1-\dsp\frac{x}{2}$} \end{lapdf} $f_{k}(x)=e^{\dsp{2k-x}}+x-3k$ \qquad $k = -1 \dots +3$ \end{center} \end{document}