Lösungen/Solutions/I1S1Ue/Ex8

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

Ueb/Ex 1      W

Gerade/ Paire

Plot[
        E^(x^2 - Cos[2  x]), {x, -1.2, 1.2}];

Ueb/Ex 2      W

f[x_] := E^(-x^2)

Solve[y == f[x], {x}]

p1 = Plot[{f[x], x}, {x, 0, 4}];

p2 = ParametricPlot[{f[x], x}, {x, 0, 4}];

Show[p1, p2, AspectRatio -> 1];

FindRoot[f[x] == 0.5, {x, 0.5}]

Ueb/Ex 3      W

Log[x^2] + Log[1/x] - Log[x]

log[x_^2] := 2 log[x];  log[1/x_] := -log[x];

log[x^2] + log[1/x] - log[x]

Ueb/Ex 4      W

Sin[x + Pi/3]

sin[x_ + y_] := Sin[x] Cos[y]  +  Cos[x] Sin[y]

sin[x + Pi/3]

cos[x_ + y_] :=  Cos[x]^2  +   Sin[y]^2

tan[x_ + y_] := sin[x + y]/cos[x + y]

tan[x + Pi/3]

tan[x + Pi/3] // TrigReduce

Ueb/Ex 5      W

a

ParametricPlot[{Cos[x] (1 + Cos[x/2]), 
          Sin[x] (1 + Cos[x/2])}, {x, 0, 2  Pi}];

ParametricPlot[{Cos[x] (1 + Cos[x/2]), 
          Sin[x] (1 + Cos[x/2])}, {x, 0, 4  Pi}];

b

<< Graphics`Graphics`

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

Ueb/Ex 6      W

Solve[2 3^x  == 5^x, {x}]

N[%]

Ueb/Ex 7      W

Solve[999  x == 367, x]

1000  a  - a  == 367  //  Solve

Ueb/Ex 8      W

Limit[Sin[3 Pi  +  4/5 n^2]/n^2, n -> Infinity]

Ueb/Ex 9      W

Limit[(n^2 - 2  n + 5)/(n^3 + n^2 + 1), 
      n -> Infinity]

Ueb/Ex 10      W

Limit[Log[n]/n^2, n -> Infinity]

Ueb/Ex 11      W

Limit[(1 + 1/n + 1/n^2) (5 + (2 + n)/n), 
      n -> Infinity]

Ueb/Ex 12      W

Limit[E^(Sin[Pi + 1/n]), n -> Infinity]