Lösungen/Solutions/B2S1Ue/Ex13

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

Ueb/Ex 1      W

a1[
          n_] := (Sin[φ]^2  +  Cos[φ]^2  +  
              3  n)/(4  n);
a1[n]

TrigReduce[a1[n]]

Limit[a1[n], n -> Infinity]

Ueb/Ex 2      W

a2[
          n_] := (6  n^3 - 5  n^2 + 2  n - 6 + 1/n)/(2  n^3 - 4  n + 
              7 + 8/n);
a2[n]

Simplify[a2[n]]

Expand[Numerator[a2[n]] * 1/n^3]/
      Expand[Denominator[a2[n]] * 1/n^3]

Limit[a2[n], n -> Infinity]

Ueb/Ex 3      W

a3[
          n_] := (Cos[n]^2 - Sin[n^2 - 4  n + 1]^3 + 8)/(n^2 - 
              Sin[Tan[n]]);
a3[n]

Limit[a3[n], n -> Infinity]

a31[
          n_] := (Cos[n]^2 - Sin[n^2 - 4  n + 1]^3 + 8)/(n^3 -  
              c);
Limit[a31[n], n -> Infinity]

Ueb/Ex 4      W

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

(x^2 - 1)/(x - 1)  // Simplify

Ueb/Ex 5      W

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

(x^3 - 1)/(x - 1)  // Simplify

Ueb/Ex 6      W

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

Ueb/Ex 7      W

Limit[Tan[x]/x  +  (x - 1) (x + 1), x -> 0]