Lösungen/Solutions/I1S1Ue/Ex4

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

Ueb/Ex 1   L

Ueb/Ex 2   W

a

f[1, x_] := x - Floor[x];
p[1] = 
        Plot[f[1, x],  {x, -2.5, 2.5}, 
          AspectRatio -> 1/5];

f[2, x_] := f[1, x - 0.5];
p[2] = 
        Plot[f[2, x],  {x, -2.5, 2.5}, 
          AspectRatio -> 1/5];

f[3, x_] := f[2, -x];
p[3] = 
        Plot[f[3, x],  {x, -2.5, 2.5}, 
          AspectRatio -> 1/5];

f[4, x_] := f[3, x + 0.5];
p[4] = 
        Plot[f[4, x],  {x, -2.5, 2.5}, 
          AspectRatio -> 1/5];

f[5, x_] := 2 f[4, 1/2 x];
p[5] = 
        Plot[f[5, x],  {x, -2.5, 2.5}, 
          AspectRatio -> 2/5];

f[6, x_] := f[5, x] - 1;
p[6] = 
        Plot[f[6, x],  {x, -2.5, 2.5}, 
          AspectRatio -> 2/5];

Show[p[6], p[1]];

f[7, x_] := f[1, x] + f[6, x]; 
    p[7] = Plot[f[7, x],  {x, -2.5, 2.5}, 
        AspectRatio -> 1/5];

f[8, x_] := 2 f[7, x] - 1;
p[8] = 
        Plot[f[8, x],  {x, -4.5, 4.5}, 
          PlotStyle -> Thickness[0.01], 
          AspectRatio -> 2/5 ];

b

Plot[Sign[Sin[x Pi]], {x, -4, 4}, 
        PlotPoints -> 100];

Lösungen/Solutions/I1S1Ue/Ex5

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

Ueb/Ex 1      L

f[x_] :=  Cos[x];  g[x_] := ArcCos[x];  h[x_] :=  E^x;

a

gof[x_] := g[f[x]];  gof[x]

b

fog[x_] := f[g[x]];  fog[x]

hog[x_] := h[g[x]];  hog[x]

c

hoogof[x_] := h[gof[x]];  
    hogoof[x]

d

hogoof[x_] := hog[f[x]];  
    hogoof[x]

hogoof[x] ==  hogoof[x]

Ueb/Ex 2      W

Remove[u]

Beachte die Definition der Funktion! / Considérer la définition de la fonction!

u[t_] := 
        ArcCos[t]  /;  (0 <  t  &&  
              t  <  Pi/2);
u[t_] := 
        Cos[t]           /;  ( 
            t  ≤  0);
u[t_] := E^t  /;  (+Pi/2 <=  t);

Lücke in D(f)! / Lacune (espace) dans D(f)!

Plot[u[x], {x, -Pi, 2}];

Lücke in D(f)! / Lacune (espace) dans D(f)!

Lücke in D (f)!/
        Lacune (espace) dans D (f)!

p1 = Plot[u[x], {x, -Pi, 1}];

p2 = Plot[u[x], {x, Pi/2, 2.2}];

Show[p1, p2];

Ueb/Ex 3      W

Remove[f]

a

Remove[f];

f[x_] := Sin[Cos[x]]

Plot[f[x], {x, -15, 15}];

Plot[{f[x], f[-x]}, {x, -15, 15}];

Plot[{f[x], -f[-x]}, {x, -15, 15}];

b

Remove[f];

f[x_] := Cos[E^x]

Plot[f[x], {x, -10, 4}];

Plot[{f[x], f[-x]}, {x, -10, 4}];

c

Remove[f];

f[x_] := (2 - x)/(x^2 - 3  x + 2)

Plot[f[x], {x, -2, 4}];

Plot[{f[x], f[-x]}, {x, -2, 4}];

Plot[{f[x], f[-(x - 1) + 1]}, {x, -2, 4}];

Plot[{f[x], f[-(-(x - 1)) + 1]}, {x, -2, 
          4}];

{Numerator[f[x]], Denominator[f[x]]}

solv = Solve[Denominator[f[x]] == 0, {x}]

solv[[1]]

solv[[2]]

f[x] /. x -> c

f[x] /. solv[[1]]

f[x] /. solv[[2]]