Lösungen/Solutions/B2S1Ue/Ex14

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

Ueb/Ex 1      W

f1[x_] := Sin[x^2 - 2]/(x^2 - 2);
Plot[f1[x], {x, -3, 3}];

Limit[f1[x], x -> 1]

Ueb/Ex 2      W

f2[x_] := Tan[x]/(x^2 - 1);
Plot[f2[x], {x, -5, 5}];

Plot[f2[x], {x, -20, 20}];

Limit[f2[x], x -> 1]

Limit[f2[x], x -> -1]

Limit[f2[x], x -> Pi/2]

Limit[f2[x], x -> -Pi/2]

etc.

Ueb/Ex 3      W

Remove[f3]

f3[x_] := 
        3  /;  (x ≤ 0);
f3[x_] := 7  /;  (x >= 6);
Plot[f3[x], {x, -3, 9}, PlotRange -> {0, 7}];

f3[x_] := 
        3  /;  (x ≤ 0);
f3[x_] := 
        3 + (7 - 3)/6 x  /;  (0 < x < 
              6);
f3[x_] := 7  /;  (x >= 6);
Plot[f3[x], {x, -2, 9}];

Ueb/Ex 4      W

Plot[E^x - 1, {x, -1, 5}];

Plot[Log[x + 1], {x, -1, 5}];

f4[
          x_] := (E^x - 1)/(Log[x + 1]);
Plot[f4[x], {x, -1, 5}];

Plot[
        f4[x], {x, -1.00000000000000000000000000000000000001, -1}];

Limit[f4[x], x -> -1, Direction -> -1]

Limit[f4[x], x -> 0]

Ueb/Ex 5      W

f[x_] := (E^x - 1)/(Log[x + 1])

Plot[f[x], {x, -1, 5}];

Plot[f[x], {x, -2, 5}];

f[0]

Limit[f[x], x -> 0]