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Mathematik Für Ökonomen I: Differentialrechnung Und Integralrechnung Von Funktionen Einer Veränderlichen by R. Landtwing, M. J. Beckmann, H. P. Künzi

Mathematik Für Ökonomen I: Differentialrechnung Und Integralrechnung Von Funktionen Einer Veränderlichen

by R. Landtwing , M. J. Beckmann , H. P. Künzi
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Book cover type: Paperback
  • ISBN13: 9783540062523
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 232
  • Original Price: GBP 46.99
  • Language: German
  • Edition: 2. Aufl.
  • Item Weight: 264 grams
  • BISAC Subject(s): General

Im ersten Kapitel haben wir den Funktionsbegriff und die wichtigen Begriffe des Grenzwertes und der Stetigkeit einer Funk tion eingefuhrt. Will man die Anwendungsmoglichkeiten des Funk tionsbegriffs erweitern und seine Aussagekraft vertiefen, so mussen wir das Verhalten der Funktionen naher untersuchen. Wir mussen vor allem die Art und Weise, wie sich der Funktionswert f(x) andert, wenn x einen bestimmten Bereich durchlauft, naher be trachten. Besondere Bedeutung kommt der durchschnittlichen An derung einer Funktion in einem bestimmten Intervall zu. Unter der durchschnittlichen Anderung der Funktion f im Intervall x:::::: x + Li x verstehen wir den Quotienten f(x + Li x) - f(x) Lif(x) Lix . Lasst man die Intervallange Lix gegen 0 streben, so strebt unter .. d d D h h . Lif(x) . b. U mstan en er ure se mttswert gegen emen estImmten Grenzwert. Derartige Grenzwerte, die in der Mathematik und in der Wirtschaftswissenschaft grosse Bedeutung besitzen, bilden den Ge genstand dieses Kapitels. 2.2 Der Differentialquotient 2.2.1 Definition des Differentialquotienten Die Funktion f sei im Intervall a::: x::: b definiert. Sind x und x + Li x zwei Punkte des Intervalls, so betrachten wir zunachst die 00 Lif(x) f(x + Lix) - f(x) durchschmtthche Anderung = Lix von f 1m Intervall x:::::: x+Lix (bzw. x+Lix:::::: x). Lif(x) Man nennt auch einen DijJerenzenquotienten von f an der Stelle x. Lix 67 Die geometrische Bedeutung des Differenzenquotienten lasst sich aus der Abb. 46 leicht ablesen. Es gilt: tgtp = Af(x) ."

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