Lösungen/Solutions/E1S1AnUe/Ex7

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

Ueb/Ex 1      W

a

Plot[{Sinh[x], Cosh[x], Tanh[x], 
          Coth[x]}, {x, -3, 3}];

b

Plot[{0.5^x, 1^x, 2^x, E^x}, {x, -2, 
          2}];

c

Plot[{0.5^-x, 1^-x, 2^-x, 
          E^-x}, {x, -2, 2}];

d

?Log

Plot[{Log[0.5, x], Log[2, x], Log[3, x], 
          Log[x]}, {x, 0.1, 2}];

Ueb/Ex 2      W

a

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

b

Plot[
        Sin[Sinh[x]], {x, -5.5, 5.5}];

c

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

d

Plot[Sinh[ArcCos[x]], {x, -1, 1}];

Ueb/Ex 3      W

===>             x==1+1/(1+x)

s = Solve[x == 1 + 1/(1 + x), {x}]

Ueb/Ex 4      W

a

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

b

Limit[Sum[1/n (2/3)^n, {k, 0, n}], n -> Infinity]

Limit[Sum[1/n (2/3)^k, {k, 0, n}], n -> Infinity]

Limit[Sum[1/k (2/3)^k, {k, 0, n}], n -> Infinity]

Ueb/Ex 5      W

a

Remove[x]

Limit[Tan[x]/x, x -> 0]

b

Limit[3/(x^2 - x), x -> Infinity]

c

Limit[(3  x^2 + 2  x)/(4  x^2 + 3  x), 
      x -> Infinity]

d

Limit[Log[x]/(x^2), x -> Infinity]

Ueb/Ex 6      W

Nicht definiert, falls Nenner = 0

Ueb/Ex 7      W

a

Limit[Abs[x]/x, x -> 0, Direction -> -1]

Limit[Abs[x]/x, x -> 0, Direction -> 1]