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Zuletzt geändert von Holger Engels am 2025/10/13 13:35
Von Version 11.1
bearbeitet von Holger Engels
am 2025/10/13 13:22
Änderungskommentar: Neues Bild Differenzierbar Hyperbel.svg hochladen
Auf Version 7.1
bearbeitet von Holger Engels
am 2025/10/13 12:39
Änderungskommentar: Neues Bild Peter.svg hochladen

Zusammenfassung

Details

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Inhalt
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8 8  {{/aufgabe}}
9 9  
10 10  {{aufgabe id="Blitzer" afb="" kompetenzen="" quelle="Kim Fujan" zeit="" cc="by-sa" tags=""}}
11 -[[image:Peter.svg||style="float:right; width:350px"]]Peter Planlos hat es, wie üblich, sehr eilig nach Hause zu kommen. Er braucht für eine 2,5 km lange Ortsdurchfahrt nur 3 Minuten und vergisst mal wieder, dass dort ein Blitzer steht. Nach 1,5 Minuten Fahrtzeit wird die Geschwindigkeit gemessen.
11 +Peter Planlos hat es, wie üblich, sehr eilig nach Hause zu kommen. Er braucht für eine 2,5 km lange Ortsdurchfahrt nur 3 Minuten und vergisst mal wieder, dass dort ein Blitzer steht. Nach 1,5 Minuten Fahrtzeit wird die Geschwindigkeit gemessen.
12 12  Seine Zeit-Weg-Funktion ist durch {{formula}}f(t)=-\frac{5}{27}t^3+\frac{5}{6}t^2{{/formula}} gegeben.
13 +[[image:Peter.svg||style="float:right; width:350px"]]
13 13  (%class=abc%)
14 14  1. Berechne seine durchschnittliche Geschwindigkeit für die Ortsdurchfahrt.
15 15  1. Muss Peter jetzt mit einem Strafzettel rechnen? Erläutere!
16 16  {{/aufgabe}}
17 17  
18 -{{aufgabe id="Differentialquotient A" afb="II" kompetenzen="K5" quelle="Holger Engels, Kim Fujan" zeit="" cc="by-sa" tags=""}}
19 -Berechne den Differentialquotienten an der Stelle {{formula}}x_0=1{{/formula}} für folgende Funktionen:
20 -(%class=abc%)
21 -1. {{formula}}f(x)=x^2+3{{/formula}}
22 -1. {{formula}}f(x)=3\cdot x^2{{/formula}}
23 -{{/aufgabe}}
24 -
25 -{{aufgabe id="Differentialquotient B" afb="III" kompetenzen="K5" quelle="Holger Engels, Kim Fujan" zeit="" cc="by-sa" tags=""}}
26 -Berechne den Differentialquotienten für eine beliebige Stelle {{formula}}x_0{{/formula}} für folgende Funktionen:
27 -(%class=abc%)
28 -1. {{formula}}f(x)=x^2+3{{/formula}}
29 -1. {{formula}}f(x)=3\cdot x^2{{/formula}}
30 -1. {{formula}}f(x)=\sqrt(x){{/formula}}
31 -{{/aufgabe}}
32 -
33 33  {{seitenreflexion bildungsplan="3" kompetenzen="3" anforderungsbereiche="3" kriterien="3" menge="3"/}}
Differenzierbar Betrag.svg
Author
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1 -XWiki.holgerengels
Größe
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1 -19.6 KB
Inhalt
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Differenzierbar Hyperbel.svg
Author
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1 -XWiki.holgerengels
Größe
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1 -22.6 KB
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Differenzierbar Logarithmus.svg
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