Lösungen/Solutions/I1S1Ue/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

?Limit

a

Limit[1/(n), n -> Infinity]

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

b

Limit[2 + 1/Sqrt[n], n -> Infinity]

c

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

Apart[2 n^2/(1 + 3  n^2)]

d

Limit[(4  n^3 - 3  n + 1)/(n^4 - 2  n^2), 
      n -> Infinity]

Apart[(4  n^3 - 3  n + 1)/(n^4 - 2  n^2)]

e

Limit[Sin[n]/n, n -> Infinity]

f

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