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Tangenten und Normalen an Funktionen

Tangenten und Normalen an Funktionen


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About the Book

Skript aus dem Jahr 2010 im Fachbereich Mathematik - Analysis, Sprache: Deutsch, Abstract: Bei der Bearbeitung von Funktionen in der gymnasialen Oberstufe wird auch auf die Berechnung von Tangenten und Normalen an den Graphen einer Funktion eingegangen. Wird ein Punkt in der Form P(x/f(x)) vorgegeben, so stellt es in der Regel kein Problem für die Schüler dar, über die Punkt-Steigungs-Form die Gleichung der Tangente an die Funktion im Punkt P zu ermitteln. Auch mit der Normalen sind meist keine Probleme verbunden, sofern die Schüler die Beziehung mT*mn=-1 kennen. Deutlich mehr Schwierigkeiten treten auf, wenn der Punkt nicht mehr auf dem Graphen der Funktion liegt, sondern in allgemeiner Lage vorgegeben ist. Der Übergang P(x/f(x)) -> P(x/y) führt häufig dazu, dass für die Lösung der Aufgabe kein schlüssiges Konzept mehr erstellt werden kann. Es werden dann verschiedene Rechenwege angegangen, die, wenn überhaupt dann nur zufällig, zum richtigen Ergebnis führen. Ziel des vorliegenden Skripts ist es, den Schülern ein allgemein anwendbares Vorgehen für die Lösung dieser Problemstellungen an die Hand zu geben. Insbesondere wird hierbei darauf geachtet, dass eine immer wieder kehrende Struktur in den Aufgaben erkennbar wird und damit dem Schüler eine entsprechende Sicherheit in der folgerichtigen Bearbeitung gegeben wird. Damit ist es dann möglich, auch andere Funktionen und bisher nicht berücksichtigte Problemstellungen erfolgreich anzugehen.


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Product Details
  • ISBN-13: 9783640542635
  • Publisher: Grin Publishing
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 5 mm
  • Weight: 172 gr
  • ISBN-10: 3640542630
  • Publisher Date: 03 Mar 2010
  • Height: 210 mm
  • No of Pages: 84
  • Series Title: German
  • Sub Title: Berechnung von Tangenten und Normalen an Funktionsgraphen, die durch einen vorgegebenen Punkt verlaufen, der nicht auf dem Graphen der Funktion lieg
  • Width: 148 mm


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