lehrkraefte:blc:miniaufgaben:kw37-2019

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lehrkraefte:blc:miniaufgaben:kw37-2019 [2019/09/23 20:31] – created Ivo Blöchligerlehrkraefte:blc:miniaufgaben:kw37-2019 [2020/08/09 13:20] (current) – external edit 127.0.0.1
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 +<PRELOAD>
 +miniaufgabe.js
 +</PRELOAD>
 +
 +
 +
 +
 +==== 16. September 2019 bis 20. September 2019 ====
 +=== Dienstag 17. September 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",
 +[["$-\\frac{2}{3} \\cdot \\ln(x) \\cdot \\left(-\\frac{1}{2}x^{3}-\\frac{2}{7}x^{2}\\right)$", "$-\\frac{2}{3} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{1}{2}x^{3}-\\frac{2}{7}x^{2}\\right) + \\ln(x) \\cdot \\left(-\\frac{3}{2}x^{2}-\\frac{4}{7}x\\right)\\right) = \\frac{1}{3}x^{2}+\\frac{4}{21}x + \\ln(x) \\cdot \\left(x^{2}+\\frac{8}{21}x\\right)$"], ["$\\frac{3}{8} \\cdot \\ln(x) \\cdot \\left(-\\frac{1}{4}x-\\frac{1}{4}\\right)$", "$\\frac{3}{8} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{1}{4}x-\\frac{1}{4}\\right) + \\ln(x) \\cdot \\left(-\\frac{1}{4}\\right)\\right) = -\\frac{3}{32}-\\frac{3}{32}\\frac{1}{x} + \\ln(x) \\cdot \\left(-\\frac{3}{32}\\right)$"], ["$\\frac{3}{4} \\cdot \\ln(x) \\cdot \\left(-\\frac{2}{3}x^{4}+\\frac{3}{2}\\right)$", "$\\frac{3}{4} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{2}{3}x^{4}+\\frac{3}{2}\\right) + \\ln(x) \\cdot \\left(-\\frac{8}{3}x^{3}\\right)\\right) = -\\frac{1}{2}x^{3}+\\frac{9}{8}\\frac{1}{x} + \\ln(x) \\cdot \\left(-2x^{3}\\right)$"], ["$\\frac{1}{3} \\cdot \\ln(x) \\cdot \\left(-\\frac{1}{8}x+\\frac{1}{8}\\right)$", "$\\frac{1}{3} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{1}{8}x+\\frac{1}{8}\\right) + \\ln(x) \\cdot \\left(-\\frac{1}{8}\\right)\\right) = -\\frac{1}{24}+\\frac{1}{24}\\frac{1}{x} + \\ln(x) \\cdot \\left(-\\frac{1}{24}\\right)$"], ["$-\\frac{2}{7} \\cdot \\ln(x) \\cdot \\left(\\frac{1}{3}x^{2}-\\frac{1}{6}x\\right)$", "$-\\frac{2}{7} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{1}{3}x^{2}-\\frac{1}{6}x\\right) + \\ln(x) \\cdot \\left(\\frac{2}{3}x-\\frac{1}{6}\\right)\\right) = -\\frac{2}{21}x+\\frac{1}{21} + \\ln(x) \\cdot \\left(-\\frac{4}{21}x+\\frac{1}{21}\\right)$"], ["$-\\frac{1}{2} \\cdot \\ln(x) \\cdot \\left(-\\frac{1}{3}x^{4}+\\frac{1}{8}x^{2}\\right)$", "$-\\frac{1}{2} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{1}{3}x^{4}+\\frac{1}{8}x^{2}\\right) + \\ln(x) \\cdot \\left(-\\frac{4}{3}x^{3}+\\frac{1}{4}x\\right)\\right) = \\frac{1}{6}x^{3}-\\frac{1}{16}x + \\ln(x) \\cdot \\left(\\frac{2}{3}x^{3}-\\frac{1}{8}x\\right)$"], ["$\\frac{4}{3} \\cdot \\ln(x) \\cdot \\left(-\\frac{1}{2}x^{4}+\\frac{1}{2}x^{2}\\right)$", "$\\frac{4}{3} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{1}{2}x^{4}+\\frac{1}{2}x^{2}\\right) + \\ln(x) \\cdot \\left(-2x^{3}+x\\right)\\right) = -\\frac{2}{3}x^{3}+\\frac{2}{3}x + \\ln(x) \\cdot \\left(-\\frac{8}{3}x^{3}+\\frac{4}{3}x\\right)$"], ["$\\frac{1}{5} \\cdot \\ln(x) \\cdot \\left(\\frac{2}{9}x^{3}-\\frac{4}{9}x^{2}\\right)$", "$\\frac{1}{5} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{2}{9}x^{3}-\\frac{4}{9}x^{2}\\right) + \\ln(x) \\cdot \\left(\\frac{2}{3}x^{2}-\\frac{8}{9}x\\right)\\right) = \\frac{2}{45}x^{2}-\\frac{4}{45}x + \\ln(x) \\cdot \\left(\\frac{2}{15}x^{2}-\\frac{8}{45}x\\right)$"], ["$-\\frac{4}{9} \\cdot \\ln(x) \\cdot \\left(-\\frac{3}{5}x^{2}+\\frac{1}{4}x\\right)$", "$-\\frac{4}{9} \\cdot \\left( \\frac{1}{x} \\cdot \\left(-\\frac{3}{5}x^{2}+\\frac{1}{4}x\\right) + \\ln(x) \\cdot \\left(-\\frac{6}{5}x+\\frac{1}{4}\\right)\\right) = \\frac{4}{15}x-\\frac{1}{9} + \\ln(x) \\cdot \\left(\\frac{8}{15}x-\\frac{1}{9}\\right)$"], ["$-\\frac{4}{9} \\cdot \\ln(x) \\cdot \\left(\\frac{1}{3}x^{4}+\\frac{1}{3}x^{2}\\right)$", "$-\\frac{4}{9} \\cdot \\left( \\frac{1}{x} \\cdot \\left(\\frac{1}{3}x^{4}+\\frac{1}{3}x^{2}\\right) + \\ln(x) \\cdot \\left(\\frac{4}{3}x^{3}+\\frac{2}{3}x\\right)\\right) = -\\frac{4}{27}x^{3}-\\frac{4}{27}x + \\ln(x) \\cdot \\left(-\\frac{16}{27}x^{3}-\\frac{8}{27}x\\right)$"]],
 +" <br> ");
 +</JS>
 +<HTML>
 +<div id="exoprodlnpoly"></div>
 +
 +</HTML>
 +<hidden Lösungen>
 +<HTML>
 +<div id="solprodlnpoly"></div>
 +</HTML>
 +</hidden>
 +
 +
 +=== Donnerstag 19. September 2019 ===
 +Prüfung, keine Miniaufgabe.