lehrkraefte:blc:miniaufgaben:kw08-2019

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lehrkraefte:blc:miniaufgaben:kw08-2019 [2019/02/26 08:05] – created Ivo Blöchligerlehrkraefte:blc:miniaufgaben:kw08-2019 [2020/08/09 13:40] (current) – external edit 127.0.0.1
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 +
 +<PRELOAD>
 +miniaufgabe.js
 +</PRELOAD>
 +
 +
 +==== 25. Februar 2019 bis 1. März 2019 ====
 +=== Mittwoch 27. Februar 2019 ===
 +Leiten Sie von Hand und ohne Unterlagen ab:
 +<JS>miniAufgabe("#exoprodtrigpoly","#solprodtrigpoly",
 +[["$-\\frac{1}{5} \\cdot \\sin(x) \\cdot \\left(\\frac{1}{2}x^{4}-\\frac{1}{2}x^{3}\\right)$", "$-\\frac{1}{5} \\cdot \\left( \\cos(x) \\cdot \\left(\\frac{1}{2}x^{4}-\\frac{1}{2}x^{3}\\right) + \\sin(x) \\cdot \\left(2x^{3}-\\frac{3}{2}x^{2}\\right)\\right)$"], ["$-\\frac{3}{7} \\cdot \\sin(x) \\cdot \\left(\\frac{4}{3}x^{2}-\\frac{1}{2}x\\right)$", "$-\\frac{3}{7} \\cdot \\left( \\cos(x) \\cdot \\left(\\frac{4}{3}x^{2}-\\frac{1}{2}x\\right) + \\sin(x) \\cdot \\left(\\frac{8}{3}x-\\frac{1}{2}\\right)\\right)$"], ["$-\\frac{2}{3} \\cdot \\sin(x) \\cdot \\left(\\frac{1}{8}x^{3}+\\frac{2}{3}x^{2}\\right)$", "$-\\frac{2}{3} \\cdot \\left( \\cos(x) \\cdot \\left(\\frac{1}{8}x^{3}+\\frac{2}{3}x^{2}\\right) + \\sin(x) \\cdot \\left(\\frac{3}{8}x^{2}+\\frac{4}{3}x\\right)\\right)$"], ["$\\frac{2}{3} \\cdot \\cos(x) \\cdot \\left(-\\frac{3}{8}x^{4}-\\frac{1}{5}x^{3}\\right)$", "$\\frac{2}{3} \\cdot \\left( (-\\sin(x)) \\cdot \\left(-\\frac{3}{8}x^{4}-\\frac{1}{5}x^{3}\\right) + \\cos(x) \\cdot \\left(-\\frac{3}{2}x^{3}-\\frac{3}{5}x^{2}\\right)\\right)$"], ["$-\\frac{2}{9} \\cdot \\sin(x) \\cdot \\left(-\\frac{2}{3}x^{4}+\\frac{1}{6}x^{2}\\right)$", "$-\\frac{2}{9} \\cdot \\left( \\cos(x) \\cdot \\left(-\\frac{2}{3}x^{4}+\\frac{1}{6}x^{2}\\right) + \\sin(x) \\cdot \\left(-\\frac{8}{3}x^{3}+\\frac{1}{3}x\\right)\\right)$"], ["$\\frac{1}{8} \\cdot \\sin(x) \\cdot \\left(\\frac{1}{3}x^{3}-\\frac{2}{3}\\right)$", "$\\frac{1}{8} \\cdot \\left( \\cos(x) \\cdot \\left(\\frac{1}{3}x^{3}-\\frac{2}{3}\\right) + \\sin(x) \\cdot \\left(x^{2}\\right)\\right)$"], ["$\\frac{1}{3} \\cdot \\cos(x) \\cdot \\left(-\\frac{1}{2}x^{3}-\\frac{1}{6}x\\right)$", "$\\frac{1}{3} \\cdot \\left( (-\\sin(x)) \\cdot \\left(-\\frac{1}{2}x^{3}-\\frac{1}{6}x\\right) + \\cos(x) \\cdot \\left(-\\frac{3}{2}x^{2}-\\frac{1}{6}\\right)\\right)$"], ["$\\frac{2}{3} \\cdot \\cos(x) \\cdot \\left(\\frac{1}{8}x^{2}+\\frac{1}{5}\\right)$", "$\\frac{2}{3} \\cdot \\left( (-\\sin(x)) \\cdot \\left(\\frac{1}{8}x^{2}+\\frac{1}{5}\\right) + \\cos(x) \\cdot \\left(\\frac{1}{4}x\\right)\\right)$"], ["$\\frac{3}{4} \\cdot \\cos(x) \\cdot \\left(\\frac{3}{7}x^{3}+\\frac{4}{9}x\\right)$", "$\\frac{3}{4} \\cdot \\left( (-\\sin(x)) \\cdot \\left(\\frac{3}{7}x^{3}+\\frac{4}{9}x\\right) + \\cos(x) \\cdot \\left(\\frac{9}{7}x^{2}+\\frac{4}{9}\\right)\\right)$"], ["$\\frac{3}{7} \\cdot \\cos(x) \\cdot \\left(\\frac{1}{2}x^{4}-\\frac{1}{3}\\right)$", "$\\frac{3}{7} \\cdot \\left( (-\\sin(x)) \\cdot \\left(\\frac{1}{2}x^{4}-\\frac{1}{3}\\right) + \\cos(x) \\cdot \\left(2x^{3}\\right)\\right)$"]],
 +" <br> ");
 +</JS>
 +<HTML>
 +<div id="exoprodtrigpoly"></div>
 +
 +</HTML>
 +<hidden Lösungen>
 +<HTML>
 +<div id="solprodtrigpoly"></div>
 +</HTML>
 +</hidden>
 +
 +
 +=== Freitag 1. März 2019 ===
 +
 +Leiten Sie von Hand und ohne Unterlagen ab. Geben Sie das Resultat in der Form "Polynom + $ln(x)$ mal Polynom" an.
 +<JS>miniAufgabe("#exoprodlnpoly","#solprodlnpoly",
 +[["$-\\frac{1}{6} \\cdot \\ln(x) \\cdot \\left(\\frac{4}{9}x-\\frac{3}{2}\\right)$", "$-\\frac{1}{6} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{4}{9}x-\\frac{3}{2}\\right) + \\ln(x) \\cdot \\left(\\frac{4}{9}\\right)\\right) = -\\frac{2}{27}+\\frac{1}{4}\\frac{1}{x^1} + \\ln(x) \\cdot \\left(-\\frac{2}{27}\\right)$"], ["$-\\frac{1}{2} \\cdot \\ln(x) \\cdot \\left(\\frac{3}{7}x^{2}-\\frac{3}{4}x\\right)$", "$-\\frac{1}{2} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{3}{7}x^{2}-\\frac{3}{4}x\\right) + \\ln(x) \\cdot \\left(\\frac{6}{7}x-\\frac{3}{4}\\right)\\right) = -\\frac{3}{14}x+\\frac{3}{8} + \\ln(x) \\cdot \\left(-\\frac{3}{7}x+\\frac{3}{8}\\right)$"], ["$-\\frac{1}{7} \\cdot \\ln(x) \\cdot \\left(-\\frac{2}{3}x^{3}+\\frac{1}{2}x^{2}\\right)$", "$-\\frac{1}{7} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{2}{3}x^{3}+\\frac{1}{2}x^{2}\\right) + \\ln(x) \\cdot \\left(-2x^{2}+x\\right)\\right) = \\frac{2}{21}x^{2}-\\frac{1}{14}x + \\ln(x) \\cdot \\left(\\frac{2}{7}x^{2}-\\frac{1}{7}x\\right)$"], ["$-\\frac{1}{3} \\cdot \\ln(x) \\cdot \\left(\\frac{1}{2}x^{3}+\\frac{2}{3}\\right)$", "$-\\frac{1}{3} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{1}{2}x^{3}+\\frac{2}{3}\\right) + \\ln(x) \\cdot \\left(\\frac{3}{2}x^{2}\\right)\\right) = -\\frac{1}{6}x^{2}-\\frac{2}{9}\\frac{1}{x^1} + \\ln(x) \\cdot \\left(-\\frac{1}{2}x^{2}\\right)$"], ["$-\\frac{1}{2} \\cdot \\ln(x) \\cdot \\left(-\\frac{3}{5}x^{2}-\\frac{4}{3}\\right)$", "$-\\frac{1}{2} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{3}{5}x^{2}-\\frac{4}{3}\\right) + \\ln(x) \\cdot \\left(-\\frac{6}{5}x\\right)\\right) = \\frac{3}{10}x+\\frac{2}{3}\\frac{1}{x^1} + \\ln(x) \\cdot \\left(\\frac{3}{5}x\\right)$"], ["$-\\frac{3}{4} \\cdot \\ln(x) \\cdot \\left(\\frac{2}{9}x^{2}-\\frac{1}{7}x\\right)$", "$-\\frac{3}{4} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{2}{9}x^{2}-\\frac{1}{7}x\\right) + \\ln(x) \\cdot \\left(\\frac{4}{9}x-\\frac{1}{7}\\right)\\right) = -\\frac{1}{6}x+\\frac{3}{28} + \\ln(x) \\cdot \\left(-\\frac{1}{3}x+\\frac{3}{28}\\right)$"], ["$\\frac{1}{2} \\cdot \\ln(x) \\cdot \\left(\\frac{4}{7}x+\\frac{1}{4}\\right)$", "$\\frac{1}{2} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{4}{7}x+\\frac{1}{4}\\right) + \\ln(x) \\cdot \\left(\\frac{4}{7}\\right)\\right) = \\frac{2}{7}+\\frac{1}{8}\\frac{1}{x^1} + \\ln(x) \\cdot \\left(\\frac{2}{7}\\right)$"], ["$-\\frac{1}{2} \\cdot \\ln(x) \\cdot \\left(\\frac{1}{5}x^{4}+\\frac{3}{7}x\\right)$", "$-\\frac{1}{2} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{1}{5}x^{4}+\\frac{3}{7}x\\right) + \\ln(x) \\cdot \\left(\\frac{4}{5}x^{3}+\\frac{3}{7}\\right)\\right) = -\\frac{1}{10}x^{3}-\\frac{3}{14} + \\ln(x) \\cdot \\left(-\\frac{2}{5}x^{3}-\\frac{3}{14}\\right)$"], ["$\\frac{1}{4} \\cdot \\ln(x) \\cdot \\left(\\frac{4}{9}x^{3}-\\frac{2}{5}x^{2}\\right)$", "$\\frac{1}{4} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{4}{9}x^{3}-\\frac{2}{5}x^{2}\\right) + \\ln(x) \\cdot \\left(\\frac{4}{3}x^{2}-\\frac{4}{5}x\\right)\\right) = \\frac{1}{9}x^{2}-\\frac{1}{10}x + \\ln(x) \\cdot \\left(\\frac{1}{3}x^{2}-\\frac{1}{5}x\\right)$"], ["$-\\frac{1}{2} \\cdot \\ln(x) \\cdot \\left(-\\frac{3}{2}x^{3}-\\frac{3}{4}x^{2}\\right)$", "$-\\frac{1}{2} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{3}{2}x^{3}-\\frac{3}{4}x^{2}\\right) + \\ln(x) \\cdot \\left(-\\frac{9}{2}x^{2}-\\frac{3}{2}x\\right)\\right) = \\frac{3}{4}x^{2}+\\frac{3}{8}x + \\ln(x) \\cdot \\left(\\frac{9}{4}x^{2}+\\frac{3}{4}x\\right)$"]],
 +" <br> ");
 +</JS>
 +<HTML>
 +<div id="exoprodlnpoly"></div>
 +
 +</HTML>
 +<hidden Lösungen>
 +<HTML>
 +<div id="solprodlnpoly"></div>
 +</HTML>
 +</hidden>
 +
 +