Änderungen von Dokument BPE 13.1 Bestandsrekonstruktion und Orientierter Flächeninhalt

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  • Streifenmethode.ggb
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52	52	{{aufgabe id="Streifenmethode" afb="II" kompetenzen="" quelle="Holger Engels, Stefanie Walz" zeit=""}}
53	53	[[Streifenmethode.svg||width=300 class=right]]Das Schaubild zeigt die Normalparabel {{formula}}f(x)= x^2{{/formula}}. Für //n// Streifen und einer Streifenbreite von {{formula}}\frac{b}{n}{{/formula}} ergibt sich die Untersumme folgendermaßen:
54	54
55		-{{formula}}U_n = \Delta x \cdot f(1\cdot\Delta x) + \Delta x \cdot f(2\cdot\Delta x) + ... + \Delta x \cdot f(n\cdot\Delta x){{/formula}}
56		-{{formula}}U_n = \Delta x \cdot (1\cdot \Delta x)^2 + \Delta x \cdot (2\cdot \Delta x)^2 + ... + \Delta x \cdot (n\cdot \Delta x)^2{{/formula}}
	55	+{{formula}}
	56	+\begin{aligned}
	57	+U_n = \Delta x \cdot f(1\cdot\Delta x) + \Delta x \cdot f(2\cdot\Delta x) + ... + \Delta x \cdot f(n\cdot\Delta x) \\
	58	+&=& \Delta x \cdot (1\cdot \Delta x)^2 + \Delta x \cdot (2\cdot \Delta x)^2 + ... + \Delta x \cdot (n\cdot \Delta x)^2
	59	+\end{aligned}
	60	+{{/formula}}
	61	+
57	57	... führt schließlich zu ...
	63	+
58	58	{{formula}}U_n = b^3\frac16(2+\frac3n+\frac1{n^2}){{/formula}}
	65	+
59	59	Berechne den Wert der Summe für unterschiedliche //n//.
60	60	(%class="border slim"%)
61	61	|=n| 4 | 8 | 100
62	62	|={{formula}}U_n{{/formula}}|||
63		-Betrachte den Term und begründe, gegen welchen Wert er für {{formula}}n\rightarrow}infty{{/formula}} strebt.
	70	+Betrachte den Term und begründe, gegen welchen Wert er für {{formula}}n\rightarrow\infty{{/formula}} strebt.
64	64	{{/aufgabe}}
65	65
66	66	== Bestimmtes Integral ==

Streifenmethode.ggb

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Streifenmethode.svg

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