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2.04 Td ()Tj 1 0 0 1 80.16 558.8 Tm ( )Tj ] /Count 4 145.8 0.12 Td (3)Tj /R7 9.98676 Tf [( )-2.63158(3)-5.26316(\))-3.84164( )250]TJ 1 0 0 1 240.72 677.72 Tm 27.24 4.56 Td W n S 47 0 obj /R7 6.48 Tf ET /R7 6.48 Tf (t)Tj f f /R7 9.98676 Tf ( )Tj [(4 )250]TJ Illustrierende Aufgaben zum LehrplanPLUS Fach- und Berufsoberschule, Mathematik, Jahrgangsstufen 11 und 12 Seite 1 von 6 Ganzrationale Funktionen Stand: 10.05.2019 Jahrgangsstufen FOS 11, BOS 12 Fach/Fächer Mathematik Übergreifende Bildungs- und Erziehungsziele Zeitrahmen 45 Minuten Benötigtes Material Die Aufgabe soll ohne Verwendung von Hilfsmitteln gelöst werden. -385.8 -26.04 Td ( )Tj ET W n -245.52 -12.36 Td (2)Tj /R7 6.48 Tf 1.8 1.56 Td 4413 4651.67 l 1 0 0 1 543.6 58.2802 Tm f 1 0 0 1 370.44 545.6 Tm 3.24 -4.56 Td /R7 6.48 Tf 1 0 0 1 124.44 229.76 Tm (3)Tj 10.2 4.56 Td 7.92 4.56 Td (t)Tj 1 0 0 1 380.76 468.32 Tm /R7 9.98676 Tf /R7 6.48 Tf 4.92 4.56 Td 1 0 0 1 393.72 480.68 Tm f 160.56 -1.56 Td 1260 1263.67 l 2681 4045.67 l 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0 0 8.33333 0 0 cm BT Q (,)Tj [( )-2.33366(8)-4.66829( )-8785.96(k)7.3486(\))-3.44696( )-338.781(f)]TJ [( )-2.33366(8)-4.66829( )-10672.5(h)7.3486(\))-3.44696( )-338.781(f)]TJ 8.33333 0 0 8.33333 0 0 cm BT (1)Tj /R7 10.0134 Tf 2.52 0 Td (6)Tj /R15 9.96 Tf 10.92 0 Td Q 8.33333 0 0 8.33333 0 0 cm BT f 7.92 0 Td /R8 9.96 Tf q [( )-2.33512(+)-0.748061( )-2.33512(2)-4.66731(x)500]TJ [( )-2.37067(+)-0.830321( )-2.37067(2)-4.74134(t)1.59316(\))333]TJ /R15 9.96 Tf 2898 3957.67 6 6 re /R7 9.98676 Tf [( )-2.63158(2)-5.26316(x)500]TJ [( )-2.33439(+)-0.748061( )-2.33366(2)-4.66878(x)500]TJ 145.8 0.12 Td /R7 9.98676 Tf ()Tj 35.04 0 Td 1 0 0 1 92.88 322.04 Tm ()Tj (1)Tj 14.16 0 Td /R11 1 Tf -336.36 -12.36 Td /R7 6.48 Tf /R15 9.96 Tf ()Tj T*[(B)-5.89098(e)-0.588915(s)4.49057(t)1.634(i)1.634(m)20.9978(m)20.9978(e)-0.588915( )-182.573(d)-4.66805(i)1.634(e)-0.588915( )-182.573(F)3.26873(u)7.34787(n)7.34713(k)7.34713(t)1.634(i)1.634(o)-4.66878(n)7.34713(s)4.4913(g)7.34713(l)1.634(e)-0.588181(i)1.634(c)-0.588181(h)7.3486(u)7.34713(n)7.34713(g)7.34713(e)-0.588181(n)7.34713( )-182.572(d)-4.66878(e)-0.588181(r)-3.44548( )-170.556(g)7.34713(a)-0.588181(n)7.34713(z)-0.588181(r)-3.44548(a)-0.589648(t)1.634(i)1.634(o)-4.66731(n)7.3486(a)-0.589648(l)1.634(e)]TJ /R7 9.98676 Tf 3.24 -4.56 Td /R11 1 Tf [(1)-6.0241(;)0.89126( )-3.01205(0)-6.0241(})-1.92665( )-3.01208( )]TJ 141.12 -1.56 Td 1 0 0 1 124.68 175.16 Tm q 0.952057 0 0 -1.04794 0 0 cm (t)Tj /R7 6.48 Tf – Ableitungen ganzrationaler Funktionen berechnen – Tangentensteigungen berechnen – Nullstellen berechnen – Extremstellen mit dem Vorzeichenwechselkriterium bestimmen – Gleichungssysteme lösen k Check-in: ob Sie die oraussetzungen 6. /R7 9.98676 Tf /R7 9.99984 Tf W n 1 0 0 1 100.56 226.16 Tm W n 15 0 Td ()Tj /R7 9.98676 Tf 2744 1105.67 l Q /R15 9.96 Tf 4.92 4.56 Td 1984 1483.67 m -350.64 -24.6 Td /R7 9.98676 Tf f /R7 9.99984 Tf W n q 0.952057 0 0 -1.04794 0 0 cm 1 0 0 1 321.96 442.04 Tm q 1 0 0 1 129.24 133.28 Tm q ET 8.33333 0 0 8.33333 0 0 cm BT 7.92 0 Td 12.48 4.56 Td 17.4 -1.56 Td -364.2 -28.08 Td ( )Tj /R7 9.975 Tf 1598 2632.67 6 6 re ()Tj 4060 4671.67 l ()Tj 11.64 0 Td /R7 9.99984 Tf 1598 3863.67 6 94 re (1)Tj 7.92 0 Td 2731 2650.67 l h ()Tj /R15 9.96 Tf W n /R7 6.48 Tf [(\()-4.35041(3)-6.0241( )250]TJ 145.8 0.12 Td ET /R7 9.98676 Tf 900 1133.67 l 1598 4457.67 6 6 re 234.96 0 Td /R7 6.48 Tf 8.33333 0 0 8.33333 0 0 cm BT q EI 3785 4651.67 l ( )Tj /R15 9.96 Tf 2933 4617.67 m /R15 9.96 Tf 7.92 0 Td /R7 9.98676 Tf /R15 9.96 Tf /R7 9.98532 Tf [( )-1.66257(5)-3.32513(\))333]TJ 3403.16 -3087.64 m /R7 9.98676 Tf [([)-3.84164(x)500]TJ 3.72 0 Td [( )-2.37067(+)-0.830321( )-2.37067(3)-4.74134(\()-3.49439(x)7.27631( )250]TJ )-2.00404( )]TJ ()Tj 8.33333 0 0 8.33333 0 0 cm BT 2997 4139.67 m h 3.36 0 Td ( )Tj 3.24 -4.56 Td -460.44 -11.28 Td W n /R7 6.48 Tf /R7 9.98532 Tf ET ()Tj [(3 )250]TJ /R7 6.48 Tf ()Tj /R7 9.98532 Tf h /R7 6.48 Tf h 10.92 0 Td (t)Tj Q 3517 4066.67 l /R15 9.96 Tf 1 0 0 1 183 398.6 Tm [(5 )250]TJ [(e)0.593931(\))-2.5504( )-385.149(f)9.4334(\()-2.55054(x)8.65808( )-1.66257(+)0.754848( )-1.66257(4)-3.32587(\))-2.55054( )250]TJ /R7 9.98676 Tf q 2713 5168.67 l q 1525 3453.67 l -60.84 -12.36 Td (\()Tj [(b)-4.74097(\))-3.49401( )-326.847(f)8.52399(\()-3.49365(x)7.27631(\))-3.49365( )-2.37067(=)-0.829587( )-2.37067(3)-4.74134(x)7.27631( )-2.37067(+)-0.829587( )-2.37067(2)-4.74102( )-1720.89(e)-0.652814(\))-3.49401( )-386.935(f)8.52326(\()-3.49439(x)7.27631(\))-3.49439( )-2.37067(=)-0.828854( )-2.37067(3)-4.74134(x)500]TJ h h /R7 9.98532 Tf q /R11 1 Tf 7.92 0 Td 15.24 0 Td ( )Tj q /R7 9.98676 Tf Q ( )Tj 3.24 -4.56 Td 1 0 0 1 302.88 385.28 Tm 1 0 0 1 98.4 468.32 Tm /R15 9.96 Tf /R7 9.96 Tf q 8.33333 0 0 8.33333 0 0 cm BT 1 0 0 1 161.88 549.8 Tm 1 0 0 1 377.52 466.76 Tm ()Tj 1 0 0 1 352.2 360.56 Tm -317.88 -26.88 Td f ()Tj Skizzieren Sie die beiden Graphen in ein gemeinsames Koordinatensystem und berechnen Sie den Inhalt der Fläche, die von f und g … f /R7 9.98676 Tf 4.92 4.56 Td ET endobj /R15 9.96 Tf 3.24 1.56 Td (2)Tj 1 0 0 1 305.4 397.64 Tm 3277 4560.67 l Q (5)Tj (2)Tj ���xMf$��L@D�f���y��d�fDy9�,=x|���f�p����y�>�Ơ���� ��� �wv�>;�Ү �*ښ^�z���$��TH �� /R15 9.96 Tf 1072 4258.67 m 3.24 -4.56 Td (2)Tj 2973 1158.67 l 8.33333 0 0 8.33333 0 0 cm BT 2898 4263.67 6 94 re /R7 9.975 Tf ��5�Sљ�|����26ӵz��D�U�U2�߂X)g�!��� �%���{ 4�h y�'���߇U�2�Œ�K�[ <>stream /R7 9.98532 Tf 817 1155.67 l /R7 9.975 Tf /R7 9.975 Tf 8.33333 0 0 8.33333 0 0 cm BT /R7 6.48 Tf ( )Tj 2189 4063.67 6 94 re 7.92 0 Td 164.76 -1.56 Td /R7 9.975 Tf /H 30 1 0 0 1 319.8 388.16 Tm /R7 9.96 Tf /R7 6.48 Tf /R7 6.48 Tf 4316.97 -4065.75 l /R7 10.0134 Tf [( )-2.63158(S)556]TJ /R7 6.48 Tf ()Tj 2921 1922.67 m 4.92 -4.56 Td 2931 4258.67 m 3868 3235.67 l 1242 4778.67 m 2898 3857.67 6 6 re /R7 6.48 Tf 3323 3235.67 l /R7 9.96 Tf 5.28 4.56 Td 0.12 0 0 -0.12 139.56 545.64 Tm /R7 6.48 Tf (2)Tj 1 0 0 1 383.28 390.32 Tm 1 0 0 1 332.88 261.2 Tm /R7 9.98676 Tf q /R7 9.98532 Tf [(\()-2.54981(x)8.65881( )250]TJ q 1 0 0 1 526.8 549.32 Tm 2898 4063.67 6 94 re /R7 9.98676 Tf [(c)-1.78326(\))-4.34944( )-388.554(f)7.69852(\()-4.34967(x)6.0241(\))-4.34967( )-3.01205(=)-2.26492( )-3.01205(\()-4.34967(x)6.0241( )-3.01205(+)-2.26492( )-3.01205(2)-6.0241(\))333]TJ (2)Tj /R7 9.98676 Tf (2)Tj /R7 9.975 Tf 1056 1566.67 m 1 0 0 1 509.16 468.32 Tm q ()Tj ET 19.08 4.56 Td /R7 6.48 Tf T*[(A)-0.891628(u)1.78326(f)-4.34967(g)-6.0241(a)-6.0241(b)1.78326(e)-1.78326( )-3.01208(1)-6.0241(2)-6.0241(:)-4.34967( )-3.01205(B)-7.69852(e)-1.78326(s)3.45768(t)-4.34894(i)0.89126(m)25.7715(m)25.7715(u)1.78252(n)1.78252(g)-6.0241( )-3.01205(v)-6.0241(o)-6.0241(n)1.78252( )-3.01205(F)-3.45768(u)1.78252(n)1.78252(k)13.8307(t)-4.34894(i)0.89126(o)-6.02263(n)1.78252(s)3.45768(g)-6.0241(l)0.89126(e)-1.78252(i)0.89126(c)-1.78252(h)1.78252(u)1.78252(n)1.78252(g)-6.0241(e)-1.78252(n)1.78306( )]TJ 81.96 4.56 Td ()Tj f Q 2983 2041.67 l f ()Tj ()Tj 8.33333 0 0 8.33333 0 0 cm BT /R7 6.48 Tf [(b)-4.66841(\))-3.44553( )-326.764(f)8.57043(\()-3.44548(x)7.34787(\))-3.44548( )-2.33439(=)-0.748061( )-2.33439(x)500]TJ [( )-2.00394(3)-4.00788(\))-3.00539( )-8234.14(h)7.99232(\))-3.00539( )-338.009(\()-3.00591(x)500.008]TJ 2733 2280.67 l ()Tj ( )Tj (2)Tj 2189 3463.67 6 6 re 3.24 -4.56 Td /R7 6.48 Tf 7.92 0 Td 4031.27 -4177.39 l 1289 3410.67 m /R7 6.48 Tf ET Q ( )Tj /R8 9.96 Tf S /R15 9.96 Tf /R7 9.98676 Tf q 3501 4151.67 l ()Tj . (2)Tj 0 G /R7 9.96 Tf 3822 3235.67 l /R7 9.98676 Tf [( )-3.01205(3)-6.0241(\))-4.34944( )-9003.01(g)6.0241(\))-4.34944( )-340.361(f)]TJ Klasse], Nullstellen; Funktion oder nicht? ( )Tj 1 0 0 1 50.4 432.2 Tm [(2 )250]TJ (2)Tj [( )-2.33512(t)1.634( )-2.33512(z)-0.589648(u)7.3486( )-2.33512(P)-8.74791(\()-3.44695(2)-4.66731(t)278]TJ [( )-2.33439(9)-4.66805(x)500]TJ 1.8 1.56 Td /R7 9.98532 Tf 3277 3326.67 m endobj [( )-2.33439(6)-4.66805(x)500]TJ h Q /R7 6.48 Tf 33.12 0 Td 1692 5944.67 m /R7 9.98676 Tf S 06.03.2019 - Nullstellen einer ganzrationalen Funktion Produktform und Linearfaktoren einer ganzrationalen Funktion Symmetrieverhalten ganzrationaler Funktionen Verhalten für \(x \to -\infty\) und \(x \to +\infty\) Beispielaufgabe Eine Funktion \(f\) mit \(f(x) = a_ Bestimmen Sie Lage und Art aller Nullstellen … 30 4.56 Td 8.33333 0 0 8.33333 0 0 cm BT 1 0 0 1 419.88 480.68 Tm /R15 9.96 Tf Q /R7 9.99984 Tf Q 33.84 -1.56 Td 1604 3957.67 585 6 re [(\()-3.44695(1)500]TJ ET 7.92 0 Td 2932 2490.67 m /R7 6.48 Tf 3.24 -4.56 Td 1 0 0 1 350.52 221.84 Tm 7.08 -6.36 Td 3515 4142.67 l /R7 6.48 Tf ()Tj 60.36 4.56 Td ( )Tj 1 0 0 1 339.96 528.2 Tm ET /R7 9.98532 Tf Q (3)Tj Ableitung von trigonometrische Funktionen Aufgaben mit Lösungen Author: Sascha Frank Subject: Ableitung Keywords: Ableitung, Aufgaben, Lösungen, trigonometrisch, Funktionen Created Date: 12/26/2016 7:49:35 PM endobj /R15 9.96 Tf 7.92 0 Td /R7 9.98676 Tf /R7 9.98532 Tf /R7 6.48 Tf 19 0 R 1 0 0 1 50.4 325.76 Tm 1.8 1.56 Td /R11 1 Tf 7.92 0 Td (4)Tj -436.8 -27.96 Td /R7 9.96 Tf /R15 9.96 Tf [(3)-3087.49(1)499.998]TJ /R15 9.96 Tf Q [( )-2.33366(1)-4.66829( )-4904.83(l)1.634(\))-3.44696( )-555.067(f)]TJ 1694 1541.67 m [(\()-3.84164(x)6.76692( )-2.63158(+)-1.41271( )-2.63158(1)-5.26316(\))-3.84164(\()-3.84164(x)6.76692( )250]TJ 4413 3326.67 l /R7 6.48 Tf /R7 9.975 Tf 2195 3232.67 348 6 re /R15 9.96 Tf f -357.72 -11.28 Td (x)Tj 2933 2055.67 l /R7 9.96 Tf 7.92 0 Td 2733 3332.67 l 3.24 -4.56 Td 3.24 1.56 Td /R7 6.48 Tf ( )Tj /R15 9.96 Tf 2979 2159.67 l /R7 6.48 Tf 8.33333 0 0 8.33333 0 0 cm BT Q /R15 9.96 Tf q /R7 9.99984 Tf 834 4151.67 m (3)Tj T*[(A)-0.891628(u)1.78326(f)-4.34967(g)-6.0241(a)-6.0241(b)1.78326(e)-1.78326( )-3.01205(7)-6.02416(:)-4.34967( )-3.01205(g)-6.0241(e)-1.78326(m)25.7708(e)-1.78326(i)0.89126(n)1.78252(s)3.45768(a)-6.0241(m)25.7715(e)-1.78252( )-3.01205(P)-3.45768(u)1.78252(n)1.78252(k)13.8307(t)-4.34894(e)-1.78319( )]TJ 3.24 -4.56 Td /R7 9.98676 Tf [( )-3.01205(3)-6.0241(\))333]TJ Q /R7 9.98532 Tf /R15 9.96 Tf (x)Tj endobj 1525 4778.67 l 3093 4151.67 l Q /R7 9.98532 Tf f 1 0 0 1 50.4 306.92 Tm [(0)-4.66731(\))-3.44695( )-2.33512(u)7.3486(n)7.3486(d)-4.66731( )-2.33512(P)556]TJ 7.92 0 Td -1.08 14.28 Td [(g)7.3486(\))-3.44696( )-338.781(f)]TJ (1)Tj 12.36 TL q /R15 9.96 Tf 4.92 -4.56 Td 775 2091.67 l 1398 5517.67 m 3378 1107.67 m f /R7 9.98532 Tf (x)Tj q /R7 9.98676 Tf ET 4.92 -4.56 Td ( )Tj 1014 4457.67 584 6 re /R7 9.99984 Tf 8.33333 0 0 8.33333 0 0 cm BT 1008 3475.67 6 94 re [(2)-28.6991(x)-1626.82(x)-1566.74(3)-4.66731(x)500]TJ 390 2532.67 618 6 re 1.8 1.56 Td 0.12 0 0 -0.12 357.72 545.64 Tm f 47.16 0 Td -307.2 -32.64 Td /R7 10.0134 Tf [( )-2.63158(1)-5.26316(\))-3.84164(\()-3.84164(x)500]TJ /R7 6.48 Tf 8.33333 0 0 8.33333 0 0 cm BT ()Tj (3)Tj 47111 1 0 0 1 159.48 147.68 Tm /R15 9.96 Tf [(S)1.78289(c)-1.78326(h)6.0241(a)-1.78326(u)6.0241(b)-6.0241(i)0.89126(l)0.89126(d)-6.0241(e)-1.78326(r)-4.34944( )-243.976(f)7.69852(�)6.0241(r)-4.34967( )-231.928(d)-6.0241(i)0.89126(e)-1.78252( )-231.928(g)6.0241(e)-1.78252(g)6.0241(e)-1.78252(b)-6.0241(e)-1.78252(n)6.0241(e)-1.78252(n)6.0241( )-231.928(t)0.89153(. Q 3.24 -4.56 Td /R7 9.98676 Tf f BI [(x)7.34713( )250]TJ ( )Tj <> 8.28 -7.32 Td f /R15 9.96 Tf 12.48 4.56 Td 1014 3569.67 584 6 re ()Tj 1 0 0 1 395.52 502.16 Tm ()Tj f <> 1 0 0 1 100.8 552.92 Tm 1.8 1.56 Td ()Tj 2.52 0 Td /R7 9.975 Tf [( )-2.00394(= )-2.00394(1)-4.00788( )-2.00394(u)7.99232(n)7.99232(d)-4.00788( )-2.00404(P)-8.00843(\()-3.00591(0)-4.00788(|)19.9969(1)-4.00788(\))-3.00539( )-11642.2(e\))-3.00539( )-386.01(n)7.99232( )-2.00394(= )-2.00394(4)-4.00788(,)-2.00394( )-2.00394(x)500.008]TJ 2189 4800.67 6 94 re [(f)7.69889(\))-4.34944( )-509.036(f)7.69852(\()-4.34967(x)6.0241(\))-4.34967( )-3.01205(=)-2.26492( )250]TJ q 2543 3238.67 6 225 re ID &��f� `���v�('���@��(7؂���q��[���a��� �`�olO��]�x`� /R7 6.48 Tf /R15 9.96 Tf 7.92 0 Td ()Tj Q 8.33333 0 0 8.33333 0 0 cm BT 1008 4057.67 6 6 re 384 4357.67 6 6 re 1 0 0 1 321.96 454.4 Tm /R15 9.96 Tf [( )-2.63158(t)1.30698( )-2.63158(+)-1.41271( )-2.63158(1)-5.26316(\))-3.84164(\()-3.84164(x)6.76692( )250]TJ /R7 9.98676 Tf /R7 6.48 Tf S 2.52 0 Td 1 0 0 1 372.72 455.96 Tm /R7 9.975 Tf f (1)Tj Q 7.92 0 Td /R7 6.48 Tf f ET /R7 9.98532 Tf -393.6 -12.36 Td 1 0 0 1 341.28 232.88 Tm f 12.48 4.56 Td 10.92 4.56 Td 2.52 0 Td (t)Tj 5.28 0 Td -398.64 -26.88 Td Ganzrationale Funktionen . /R22 9.99984 Tf (3)Tj <>stream Q (x)Tj (3)Tj Q f 8.33333 0 0 8.33333 0 0 cm BT ( )Tj (2)Tj [( )-2.33512(+)-0.748061( )250]TJ 7.92 0 Td 4.92 -4.56 Td W n [(a)-1.78326(\))-4.34944( )-388.554(f)7.69852(\()-4.34967(x)6.0241(\))-4.34967( )-3.01205(=)-2.26492( )250]TJ 1516 4563.67 l 2724 2883.67 l [( )-2.00394(+ )-2.00394(4)-4.00788(x)500.008]TJ /R7 9.975 Tf [(n)7.99723(-)8.99428(t)1.99515(en)7.99232( )-326.009(G)1.98929(r)-3.00591(ad)-4.00788(es)4.9952(,)-2.00394( )-326.009(d)-4.00788(er)-3.00591(en)7.99232( )-326.009(S)3.9903(ch)7.99232(au)7.99232(b)-4.00788(i)1.99515(l)1.99515(d)-4.00788(er)-3.00591( )-326.009(d)-4.00788(i)1.99808(e )-326.009(f)8.99428(o)-4.00788(l)1.99808(g)7.99232(en)7.99232(d)-4.00788(en)7.99232( )250]TJ /R7 6.48 Tf [(g)8.65844(\))-2.5504( )-337.213(f)9.4334(\()-2.55054(x)8.65808(\))-2.55054( )-1.66257(=)0.754848( )250]TJ /R7 9.96 Tf [(0)-4.66731(\))-3.44695( )-2.33512(u)7.3486(n)7.3486(d)-4.66731( )-2.33512(P)556]TJ 8.33333 0 0 8.33333 0 0 cm BT 1 0 0 1 363.48 385.28 Tm /R7 9.96 Tf /R11 1 Tf ()Tj 75.84 4.56 Td 0.12 0 0 -0.12 159.48 133.32 Tm /R7 9.98676 Tf Q S /R7 10.0134 Tf /R8 9.96 Tf 8.28 -7.32 Td /R15 9.96 Tf In welchen Fällen findet man Nullstellen und was bedeuten die Nullstellen in der Situation? 8.33333 0 0 8.33333 0 0 cm BT /R7 9.975 Tf 8.33333 0 0 8.33333 0 0 cm BT 1 0 0 1 395.64 454.4 Tm [(W)-5.25696(e)-0.588731(l)1.634(c)-0.588915(h)7.34787(e)-0.588915( )-2.33439(W)-5.25696(e)-0.588915(r)-3.44548(t)1.634(e)-0.588915( )-2.33439(d)-4.66805(�)7.34787(r)-3.44548(f)8.57043(e)-0.588181(n)7.34713( )-2.33366(d)-4.66878(i)1.634(e)-0.588181( )-2.33366(K)1.04582(o)-4.66878(e)-0.588181(f)8.57043(f)8.57043(i)1.634(z)-0.588181(i)1.634(e)-0.586714(n)7.34713(t)1.634(e)-0.588181(n)7.34713( )-2.33366(a)-0.588181(,)-2.33366( )-2.33366(b)-4.66878( )-2.33366(u)7.34713(n)7.34713(d)-4.66878( )-2.33366(c)-0.589648( )-2.33512(a)-0.589648(n)]TJ ()Tj 0.12 0 0 -0.12 392.28 684.36 Tm 32.52 0 Td 47.76 0 Td [( )-2.37067(t)277.999]TJ /R15 9.96 Tf (2)Tj 11.4 TL
Langhaar Collie Labrador Mix, Eine Million Mark 1923 Wert, Kindergeburtstag 11 Jährige Drinnen, Freibad Rahlstedt Tickets Kaufen, Badesalz Selber Machen Orange,