Lösungen/Solutions/E1S1AnUe/Ex2

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A=Anhang/Annexe/Appendice

Ueb/Ex 1      W

a

Plot[3 Sin[Cos[2  x^2 + 1] + 1], {x, -4, 4}];

b

Plot[Sin[x]^Cos[x], {x, -4, 4}];

c

Plot[
        Log[(x^2 + 2)/(x^4 + 2)] - x^2, {x, -2, 2}];

d

Plot[Sign[x^2 Sin[x - 1/x]], {x, -1, 1}, 
        PlotPoints -> 100];

e

Plot[x^4 - 2  x + 1, {x, -2, 2}];

f

Plot[10 Sin[x], {x, -7, 7}];

Plot[Floor[10 Sin[x]], {x, -7, 7}];

g

Plot[x + Floor[1/x + x^2], {x, -1, 3}, 
        PlotPoints -> 100];

Plot[x + Floor[1/x + x^2], {x, 0.55, 1.4}, 
        PlotPoints -> 100];

Plot[x + Floor[1/x + x^2], {x, -1, 10}, 
        PlotPoints -> 100];

h

Plot[x^x, {x, 0, 2}];

Ueb/Ex 2      L

a

Remove[PolarPlot]

polarPlot[r_, {t_, t1_, t2_}] := 
      ParametricPlot[r {Cos[t], Sin[t]}, {t, t1, t2}, 
        PlotPoints -> 100]

polarPlot[t, {t, 0, 4  Pi}];

polarPlot[2 Cos[2 t], {t, 0, Pi}];

polarPlot[2 Cos[2 t + 1], {t, 0, 2  Pi}];

polarPlot[4 + 2  Sin[4  t] + Cos[16  t], {t, 0, 2  Pi}];

polarPlot[1 + t/2 - t^2 /4, {t, 0, 2  Pi}];

Ueb/Ex 3      L

<< Graphics`ImplicitPlot`

p1 = 
        ImplicitPlot[
          Abs[x - y] == Abs[x + y] - x, {x, -10, 10}, {y, -10, 10}, 
          PlotPoints -> 200];

p2 = 
        ImplicitPlot[
          10 == Abs[Abs[x - y] - x]  Abs[x + y], {x, -10, 
            10}, {y, -10, 10}, PlotPoints -> 200];

Show[p1, p2];

{2 ≤ 1, 2 ≥ 1}

g[x_, y_] := {Abs[x - y] ≤  Abs[x + y] - x, 
        10 ≥  Abs[Abs[x - y] - x]  Abs[x + y]}

{g[-5, 0], g[-5, 3], g[-1, 0], g[-1, 2], g[-1, 5], 
      g[0, -1], g[0, 5], g[5, 5], g[10, -2]}

g1[x_, y_] := (Abs[x - y] ≤  Abs[x + y] - x); 
    g2[x_, y_] := (10 ≥  
          Abs[Abs[x - y] - x]  Abs[x + y]);

<< Graphics`InequalityGraphics`

InequalityPlot[
        g1[x, y]  &&  g2[x, y],  {x,  -4,  6},  {y, -4, 
          8} ];