February 2015
Intermediate to advanced
392 pages
17h 52m
German
Content preview from Mathematik für Wirtschaftswissenschaftler, 2nd Edition
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216 Kapitel 8. Differentialrechnung für Funktionen einer Veränderlichen
Beispiel 8.7 (Hebbare und nicht hebbare Unstetigkeit) Die Punktion /(x) = (x
3
- l)/(x
—
1)
ist für alle χ φ 1 erklärt und dort auch stetig. Das Zählerpolynom ist ohne Rest durch χ - 1 teilbar,
und daher gilt (x
3
—
l)/(x - 1) = χ
2
+ χ + 1 für ι φ 1. Der rechts stehende Term hat für χ 1 den
Grenzwert 3. Wird der Funktion /(x) für χ = 1 der Wert /( 1) = 3 zugewiesen, so ist die dann für
alle χ erklärte Punktion überall stetig. Die Unstetigkeit kann also durch Zuweisen des Grenzwertes als
Funktionswert behoben werden.
Die für χ φ 0 erklärte Funktion
8
f(x) = sin(7r/x) besitz ...
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