Änderungen von Dokument BPE 13.1 Bestandsrekonstruktion und Orientierter Flächeninhalt
Zuletzt geändert von Holger Engels am 2026/10/17 14:38
Von Version 58.6
bearbeitet von Holger Engels
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am 2026/10/12 09:31
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Auf Version 60.1
bearbeitet von Holger Engels
am 2026/10/12 10:17
am 2026/10/12 10:17
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... ... @@ -49,21 +49,27 @@ 49 49 50 50 {{formula}} 51 51 \begin{aligned} 52 -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) \\53 -\text{} &= \Delta x \cdot ( 1\cdot \Delta x)^2 + \Delta x \cdot (2\cdot \Delta x)^2 + ... + \Delta x \cdot (n\cdot \Delta x)^252 +U_n &= \Delta x \cdot f(0\cdot\Delta x) + \Delta x \cdot f(1\cdot\Delta x) + ... + \Delta x \cdot f((n-1)\cdot\Delta x) \\ 53 +\text{} &= \Delta x \cdot (0\cdot \Delta x)^2 + \Delta x \cdot (1\cdot \Delta x)^2 + ... + \Delta x \cdot ((n-1)\cdot \Delta x)^2 54 54 \end{aligned} 55 55 {{/formula}} 56 56 57 -.. .führt nach einigen Umformungen schließlich zu...57 +.. führt nach einigen Umformungen schließlich zu: 58 58 59 -{{formula}}U_n = b^3\frac16(2 +\frac3n+\frac1{n^2}){{/formula}}59 +{{formula}}U_n = b^3\frac16(2-\frac3n+\frac1{n^2}){{/formula}} 60 60 61 -Berechne den Wert dieser Summe für unterschiedliche //n//. 61 +Analog ergibt sich für die Obersumme: 62 + 63 +{{formula}}O_n = b^3\frac16(2+\frac3n+\frac1{n^2}){{/formula}} 64 + 65 +(%class=abc%) 66 +1. (((Berechne den Wert dieser Summen für unterschiedliche //n//. 62 62 (%class="border slim"%) 63 63 |=//n//| 4 | 8 | 100 64 64 |={{formula}}U_n{{/formula}}||| 65 - 66 -Betrachte den Term und begründe, gegen welchen Wert er für {{formula}}n\rightarrow\infty{{/formula}} strebt. 70 +|={{formula}}O_n{{/formula}}||| 71 +))) 72 +1. Betrachte die Terme und begründe, gegen welchen Wert beide für {{formula}}n\rightarrow\infty{{/formula}} streben. 67 67 {{/aufgabe}} 68 68 69 69 == Bestimmtes Integral ==
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