Änderungen von Dokument BPE 6.3 Momentane Änderungsrate und graphisches Ableiten
Zuletzt geändert von Stephanie Wietzorek am 2025/05/21 10:29
Von Version 98.1
bearbeitet von Stephanie Wietzorek
am 2025/05/21 09:45
am 2025/05/21 09:45
Änderungskommentar:
Neuen Anhang Beschleunigung.ggb hochladen
Auf Version 107.1
bearbeitet von Stephanie Wietzorek
am 2025/05/21 10:27
am 2025/05/21 10:27
Änderungskommentar:
Neuen Anhang Arbeitsheft 6.3. Graphisches Differenzieren L2.ggb hochladen
Zusammenfassung
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Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)
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Anhänge (0 geändert, 4 hinzugefügt, 0 gelöscht)
Details
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... ... @@ -16,16 +16,6 @@ 16 16 * Funktionsterm der Ableitungsfunktion aus Tangentensteigungen aufstellen 17 17 * Beobachtungen bei e^x 18 18 19 -{{aufgabe id="Beschleunigung" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="?"}} 20 -Ein Auto soll auf freier Autobahn auf {{formula}}180/frac{km}{h}{{/formula}} beschleunigen. Die Geschwindigkeit wird durch {{formula}}v(t)=180\cdot(1-\exp{-0,1t}){{/formula}} beschrieben. {{formula}}v(t){{/formula}} beschreibt hierbei die momentante Geschwindigkeit zum Zeitpunkt {{formula}}t{{/formula}} in Sekunden. Der Verlauf der Geschwindigkeit ist dem Schaubild zu entnehmen. 21 -[[image:Beschleunigung.svg|| width="500px"]] 22 - 23 -(%class=abc%) 24 -1. Zu welchem Zeitpunkt wird die Höchstgeschwindigkeit von {{formula}}180/frac{km}{h}{{/formula}} erreicht? 25 -1. Wann ist die Beschleunigung am höchsten? 26 -1. Skizziere ein Schaubild, aus welchem die Beschleunigung zum Zeitpunkt t hervorgeht. 27 -{{/aufgabe}} 28 - 29 29 {{aufgabe id="Tangenten einzeichnen" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="3"}} 30 30 Zeichne jeweils die Tangenten an den Stellen {{formula}}x\in\{-1, 0, 1\}{{/formula}} ein und bestimme deren Steigungen. 31 31 [[image:Tangenten einzeichnen 1.svg|| width="350px"]] [[image:Tangenten einzeichnen 2.svg|| width="350px"]] [[image:Tangenten einzeichnen 3.svg|| width="350px"]] [[image:Tangenten einzeichnen 4.svg|| width="350px"]] ... ... @@ -38,10 +38,11 @@ 38 38 39 39 {{aufgabe id="Punkte mit gegebener Steigung finden" afb="?" kompetenzen="" quelle="Stephanie Wietzorek und Simone Kanzler" cc="BY-SA" zeit="?"}} 40 40 Es ist das Schaubild {{formula}}K_f{{/formula}} einer Funktion {{formula}}f{{/formula}} gegeben. Kennzeichne Punkte auf {{formula}}K_f{{/formula}}, für die gilt: 41 - die Steigung der Tangente in diesem Punkt ist 1 42 - die Steigung der Tangente in diesem Punkt ist 1,5 43 - die Steigung der Tangente in diesem Punkt ist 0 44 - die Steigung der Tangente in diesem Punkt ist {{formula}}-\frac{17}{4}{{/formula}} 31 +(%class=abc%) 32 +1. die Steigung der Tangente in diesem Punkt ist 1 33 +1. die Steigung der Tangente in diesem Punkt ist 1,5 34 +1. die Steigung der Tangente in diesem Punkt ist 0 35 +1. die Steigung der Tangente in diesem Punkt ist {{formula}}-\frac{17}{4}{{/formula}} 45 45 [[image:Tangentensteigung.svg|| width="700px"]] 46 46 {{/aufgabe}} 47 47 ... ... @@ -51,6 +51,16 @@ 51 51 [[image:Schaubild.svg||width=500]] 52 52 {{/aufgabe}} 53 53 45 +{{aufgabe id="Beschleunigung" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="?"}} 46 +Ein Auto soll auf freier Autobahn auf {{formula}}180\frac{km}{h}{{/formula}} beschleunigen. Die Geschwindigkeit wird durch {{formula}}v(t)=180\cdot(1-e^{-0,1t}){{/formula}} beschrieben. {{formula}}v(t){{/formula}} beschreibt hierbei die momentante Geschwindigkeit zum Zeitpunkt {{formula}}t{{/formula}} in Sekunden. Der Verlauf der Geschwindigkeit ist dem Schaubild zu entnehmen. 47 +[[image:Beschleunigung.svg|| width="500px"]] 48 + 49 +(%class=abc%) 50 +1. Zu welchem Zeitpunkt wird die Höchstgeschwindigkeit von {{formula}}180\frac{km}{h}{{/formula}} erreicht? 51 +1. Wann ist die Beschleunigung am höchsten? 52 +1. Skizziere ein Schaubild, aus welchem die Beschleunigung zum Zeitpunkt t hervorgeht. 53 +{{/aufgabe}} 54 + 54 54 {{aufgabe id="Zuordnung I" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="4" interaktiv="Interaktiv Zuordnung I"}} 55 55 (% style="float:left; margin-right: 16px" %) 56 56 | [[image:Polynome zuordnen f.svg||width=200]] | | | | | [[image:Polynome zuordnen A.svg||width=200]]
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