Lösungen/Solutions/I1S1Ue/Ex2

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

Remove["Global`*"]

Ueb/Ex 1

a

Plot[3  x - 4,  {x, -2, 3}, PlotPoints -> 50];

b

Plot[Sin[Cos[x]],  {x, -2 Pi, 4  Pi}];

c

Plot[Abs[x] - Floor[Sin[x]],  {x, -14, 16}, PlotPoints -> 100];

d

Plot[Floor[4  x] - Sign[x],  {x, -2, 2}, 
        PlotPoints -> 100];

e

\(\(Plot[1/x - 1/\((x^2)\), \ {x, \(-0.5\), 0.5}, PlotPoints -> 100, 

      PlotRange -> {1, \(-20\)}]; \)\)

f

Plot[Cos[x^2 + x],  {x, -6, 6}, PlotPoints -> 100];

g

Plot[E^(-1/2 x^2),  {x, -4, 4}, PlotPoints -> 100];

h

Plot[E^( x^2),  {x, -2, 2}, PlotPoints -> 100];

i

Plot[E^(- x^2) - 1,  {x, -4, 4}, PlotPoints -> 100];

j

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

k

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

l

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

m

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

n

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

o

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

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

p

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];

q

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

Plot[x^x, {x, 0, 100}];

Ueb/Ex 2      L

Ueb/Ex 3      L

Remove[PolarPlot]

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

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

a

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

b

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

c

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

d

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

Ueb/Ex 4

Solve[x^2 - x + 1 == -x^2/2 + x + 2, {x}] // Flatten

% // N

p = 
        Plot[{x^2 - x + 1, -x^2/2 + x + 2},  {x, -4, 6}, 
          PlotPoints -> 100, DisplayFunction  ->  Identity];
Show[p, 
        Graphics[{Text["Loesung \n Solution ", {5, 5}], 
            Text["Loesung \n Solution ", {-3, 5}]}], 
        DisplayFunction  -> $DisplayFunction];

f[x_] := x^2 - x + 1; g[x_] := -x^2/2 + x + 2;

<< Graphics`InequalityGraphics`

p1 = Plot[ {f[x], g[x]},  {x,  -3,  3} ];

p2 = 
        InequalityPlot[ 
          f[x] ≥  y ≥ g[x],  {x,  -3,  
            3},  {y, -5, 12.5} ];

Show[p1, p2];