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Casio fx-7400G PLUS Manual

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Kapitel 3 Differentialrechnungen
• Um Differentialrechnungen auszuführen, zuerst das Options-Menü anzeigen und
danach die in der nachfolgenden Formel gezeigten Werte eingeben.
K2(CALC)[
1(
d/dx) f(x),a,∆ x)
Nachfolgend ist das Eingabeformat für Differentiale aufgeführt:
In dieser Definition wird der
unendlich kleine
Wert durch einen
ausreichend kleinen
Wert ∆x, ersetzt, wobei sich dieser Wert in der Nähe von f ' (a) befindet, der wie folgt
berechnet wird:
Um die bestmögliche Genauigkeit zu erhalten, verwendet diese Einheit die
Zentraldifferenz, um Differentialrechnungen auszuführen. Nachfolgend ist die
Zentraldifferenz dargestellt.
Die Neigungen an Punkt a und Punkt a + ∆x, sowie an Punkt a und Punkt a – ∆x in
der Funktion
y = f(x) sind wie folgt:
In der obigen Gleichung wird ∆
y/∆x als die Vorwärtsdifferenz bezeichnet, wogegen
∇
y/∇x als die Rückwärtsdifferenz bezeichnet wird. Um die Differentiale zu berech-
nen, verwendet die Einheit den Durchschnitt zwischen den Werten von ∆
y/∆x and
∇
y/∇x, wodurch eine höhere Genauigkeit für die Differentiale erhalten wird.
f (a + ∆x) – f (a)
f '(a) = lim –––––––––––––
∆x
∆x→0
f (a + ∆x) – f (a)
f '(a)
–––––––––––––
∆x
d
d/dx ( f (x), a, ∆x) ⇒ ––– f (a)
dx
Erhöhung/Verminderung von
x
Punkt für den Sie das Differential bestimmen
möchten.
f (a + ∆x) – f (a) ∆y f (a) – f (a – ∆x) ∇y
––––––––––––– = ––– , ––––––––––––– = –––
∆x ∆x ∆x ∇x
… 58 …


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