Beispiele/ Exemples/
E1S2AnUe/Ex1

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

Remove["Global`"]

Remove["Global`*"]

Beispiel/ Exemple 1

g[f_, x0_] := 
      Limit[(f - (f /. x -> x0))/(x - x0), 
        x -> +x0]

g[Sin[x], Pi/2]

g[Sin[x], Pi/4]

g[Sin[x], 0]

Beispiel/ Exemple 2

NIntegrate[Sin[x], {x, 0, Pi}]

Beispiel/ Exemple 3

?FindRoot

FindRoot[Sin[x] - x, {x, 1}]

Beispiel/ Exemple 4

{{x1, y1}, {x2, y2}, {x3, y3}} = {{1, 1}, {2, 3}, {3, 2}}

y2

p[x_] := a2 x^2 + a1 x + a0

{p[x1] == y1, p[x2] == y2, p[x3] == y3}

s = 
      Solve[{p[x1] == y1, p[x2] == y2, p[x3] == y3}, {a2, 
            a1, a0}] // Flatten

p1[x_] := p[x] /. s ;  p1[x]

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