Lösungen/Solutions/E1S1AnUe/Ex3

L=Lektion/Leçon-- Sprechstunde/heures de consultation
W=Work/Arbeit/Travail
Programme vgl. Ue2
Programmes voir ex2
A  =Anhang/  Annexe / Appendice

Ueb/Ex 1      L

Ueb/Ex 2      W

a

Plot[E^Cos[x], {x, 0, 20}];

b

Plot[Log[x^2/(x^2 + 1)], {x, -1.3, 1.3}];

c

f[
          x_] := -Sin[x] - 
            2  /;  (-Pi ≤  x  &&  
              x  ≤  -Pi/2);
f[x_] := 
        Sin[x]           /;  (-Pi/2 <  x  &&  
              x  ≤  +Pi/2);
f[
          x_] := -Sin[x] + 
            2  /;  (+Pi/2 <  x  &&  
              x  ≤  +Pi);

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

d

Plot[E^(-x^2), {x, -Pi, Pi}];

Ueb/Ex 3      W

a

expr = ((((4  x - 3) x + 1) x + 2) x - 5) x + 
          6;

Expand[expr]

b

4 (x - 2) (x^2 - 2  x - 5) // Expand

res = Solve[(x^2 - 2  x - 5) == 0, {x}] // Flatten

res // N

r[n_] := x /. res[[n]]

fac = 4 (x - 2) (x - r[1]) (x - r[2])

fac // Expand

c

Plot[(3  x - 
              6)/(4 (x - 2) (x^2 - 2  x - 5)), {x, -3, 
          5}];

Ueb/Ex 4      W

a

Plot[E^(-x^2), {x, -3, 3}];

E^(-x^2) = y;  x =  pm Sqrt[-Log[y]]

b

Plot[3/(x - 2), {x, -2, 2}];

y = 3/(x - 2);  x = 3/y  + 2

Ueb/Ex 4      W

a

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

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

b

polarPlot[Cos[t/2], {t, 0, 4  Pi}];

c

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