Show pageOld revisionsBacklinksBack to top This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. <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> lehrkraefte/blc/miniaufgaben/kw08-2019.txt Last modified: 2020/08/09 15:40(external edit)