Lösungen/Solutions/E1S1AnUe/Ex12

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

Ueb/Ex 1      W

Remove[A]

A[n_] := Sum[(k/n)^2 * 1/n, {k, 1, n} ]

A[n]

Limit[A[n], n -> Infinity]

Ueb/Ex 2      W

a

Limit[x Sin[x]^2/(E^x - 1)^2, x -> 0]

b

Limit[(Log[x])/(1 - Cos[x]), x -> 1]

c

Limit[(E^x - Log[x])/(x^4 - x^3), 
      x -> Infinity]

d

Limit[(x^3 - 27)/(3 - x), x -> 3]

e

Limit[(Cos[x] - Cos[Pi/4])/(Sin[x] - Sin[Pi/4]), 
      x -> Pi/4]

f

Limit[x E^(1/x), x -> 0]

g

Limit[(x^(1/3) - 1)/(x^(1/2) - 1), 
      x -> 1]