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Bei steilem Graphen wird sie durch den Nenner ",[573,1079,1081,1131],{"className":1080},[576],[573,1082,1084],{"className":1083},[580],[582,1085,1086],{"xmlns":584},[586,1087,1088,1128],{},[589,1089,1090,1094,1096,1099,1113],{},[829,1091,1093],{"stretchy":1092},"false","(",[633,1095,701],{},[829,1097,1098],{},"+",[1100,1101,1102,1105],"msup",{},[592,1103,1104],{},"f",[589,1106,1107,1110],{},[829,1108,1109],{"mathvariant":958},"′",[633,1111,1112],{},"2",[1100,1114,1115,1118],{},[829,1116,1117],{"stretchy":1092},")",[589,1119,1120,1123,1126],{},[633,1121,1122],{},"3",[592,1124,1125],{"mathvariant":958},"\u002F",[633,1127,1112],{},[596,1129,1130],{"encoding":598},"(1 + f'^2)^{3\u002F2}",[573,1132,1134,1158],{"className":1133,"ariaHidden":604},[603],[573,1135,1137,1141,1144,1147,1151,1155],{"className":1136},[608],[573,1138],{"className":1139,"style":1140},[612],"height:1em;vertical-align:-0.25em;",[573,1142,1093],{"className":1143},[723],[573,1145,701],{"className":1146},[617],[573,1148],{"className":1149,"style":1150},[853],"margin-right:0.2222em;",[573,1152,1098],{"className":1153},[1154],"mbin",[573,1156],{"className":1157,"style":1150},[853],[573,1159,1161,1165,1203],{"className":1160},[608],[573,1162],{"className":1163,"style":1164},[612],"height:1.138em;vertical-align:-0.25em;",[573,1166,1168,1172],{"className":1167},[617],[573,1169,1104],{"className":1170,"style":1171},[617,618],"margin-right:0.1076em;",[573,1173,1176],{"className":1174},[1175],"msupsub",[573,1177,1179],{"className":1178},[731],[573,1180,1182],{"className":1181},[736],[573,1183,1186],{"className":1184,"style":1185},[740],"height:0.8141em;",[573,1187,1189,1193],{"style":1188},"top:-3.063em;margin-right:0.05em;",[573,1190],{"className":1191,"style":1192},[748],"height:2.7em;",[573,1194,1196],{"className":1195},[753,754,755,756],[573,1197,1199],{"className":1198},[617,756],[573,1200,1202],{"className":1201},[617,756],"′2",[573,1204,1206,1209],{"className":1205},[806],[573,1207,1117],{"className":1208},[806],[573,1210,1212],{"className":1211},[1175],[573,1213,1215],{"className":1214},[731],[573,1216,1218],{"className":1217},[736],[573,1219,1222],{"className":1220,"style":1221},[740],"height:0.888em;",[573,1223,1224,1227],{"style":1188},[573,1225],{"className":1226,"style":1192},[748],[573,1228,1230],{"className":1229},[753,754,755,756],[573,1231,1233],{"className":1232},[617,756],[573,1234,1236],{"className":1235},[617,756],"3\u002F2"," abgeschwächt. Nur wo ",[573,1239,1241,1264],{"className":1240},[576],[573,1242,1244],{"className":1243},[580],[582,1245,1246],{"xmlns":584},[586,1247,1248,1261],{},[589,1249,1250,1257,1259],{},[1100,1251,1252,1254],{},[592,1253,1104],{},[829,1255,1109],{"mathvariant":958,"lspace":1256,"rspace":1256},"0em",[829,1258,949],{},[633,1260,635],{},[596,1262,1263],{"encoding":598},"f' = 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ist, stimmen ",[573,1327,1329,1342],{"className":1328},[576],[573,1330,1332],{"className":1331},[580],[582,1333,1334],{"xmlns":584},[586,1335,1336,1340],{},[589,1337,1338],{},[592,1339,594],{},[596,1341,599],{"encoding":598},[573,1343,1345],{"className":1344,"ariaHidden":604},[603],[573,1346,1348,1351],{"className":1347},[608],[573,1349],{"className":1350,"style":613},[612],[573,1352,594],{"className":1353},[617,618]," und 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überein.",[564,1424,1425,1426,571,1429,1528],{},"Für eine ",[568,1427,1428],{},"Parameterkurve",[573,1430,1432,1471],{"className":1431},[576],[573,1433,1435],{"className":1434},[580],[582,1436,1437],{"xmlns":584},[586,1438,1439,1468],{},[589,1440,1441,1444,1447,1449,1452,1454,1457,1460,1462,1464,1466],{},[829,1442,1093],{"fence":604,"stretchy":604,"minsize":1443,"maxsize":1443},"1.2em",[592,1445,1446],{},"x",[829,1448,1093],{"stretchy":1092},[592,1450,1451],{},"t",[829,1453,1117],{"stretchy":1092},[829,1455,1456],{"separator":604},",",[592,1458,1459],{},"y",[829,1461,1093],{"stretchy":1092},[592,1463,1451],{},[829,1465,1117],{"stretchy":1092},[829,1467,1117],{"fence":604,"stretchy":604,"minsize":1443,"maxsize":1443},[596,1469,1470],{"encoding":598},"\\bigl(x(t), 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Formel",[573,1530,1533],{"className":1531},[1532],"katex-display",[573,1534,1536,1631],{"className":1535},[576],[573,1537,1539],{"className":1538},[580],[582,1540,1542],{"xmlns":584,"display":1541},"block",[586,1543,1544,1628],{},[589,1545,1546,1548,1550],{},[592,1547,594],{},[829,1549,949],{},[697,1551,1552,1590],{},[589,1553,1554,1562,1566,1573,1576,1582,1584],{},[1555,1556,1557,1559],"mover",{"accent":604},[592,1558,1446],{},[829,1560,1561],{},"˙",[1563,1564,1565],"mtext",{}," ",[1555,1567,1568,1570],{"accent":604},[592,1569,1459],{},[829,1571,1572],{},"¨",[829,1574,1575],{},"−",[1555,1577,1578,1580],{"accent":604},[592,1579,1459],{},[829,1581,1561],{},[1563,1583,1565],{},[1555,1585,1586,1588],{"accent":604},[592,1587,1446],{},[829,1589,1572],{},[1100,1591,1592,1620],{},[589,1593,1594,1596,1606,1608,1618],{},[829,1595,1093],{"fence":604},[1100,1597,1598,1604],{},[1555,1599,1600,1602],{"accent":604},[592,1601,1446],{},[829,1603,1561],{},[633,1605,1112],{},[829,1607,1098],{},[1100,1609,1610,1616],{},[1555,1611,1612,1614],{"accent":604},[592,1613,1459],{},[829,1615,1561],{},[633,1617,1112],{},[829,1619,1117],{"fence":604},[589,1621,1622,1624,1626],{},[633,1623,1122],{},[592,1625,1125],{"mathvariant":958},[633,1627,1112],{},[596,1629,1630],{"encoding":598},"\\kappa 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= 2",[573,2719,2721,2777],{"className":2720,"ariaHidden":604},[603],[573,2722,2724,2727,2759,2762,2765,2768,2771,2774],{"className":2723},[608],[573,2725],{"className":2726,"style":2620},[612],[573,2728,2730,2733],{"className":2729},[617],[573,2731,1104],{"className":2732,"style":1171},[617,618],[573,2734,2736],{"className":2735},[1175],[573,2737,2739],{"className":2738},[731],[573,2740,2742],{"className":2741},[736],[573,2743,2745],{"className":2744,"style":1292},[740],[573,2746,2747,2750],{"style":1188},[573,2748],{"className":2749,"style":1192},[748],[573,2751,2753],{"className":2752},[753,754,755,756],[573,2754,2756],{"className":2755},[617,756],[573,2757,1421],{"className":2758},[617,756],[573,2760,1093],{"className":2761},[723],[573,2763,1446],{"className":2764},[617,618],[573,2766,1117],{"className":2767},[806],[573,2769],{"className":2770,"style":854},[853],[573,2772,949],{"className":2773},[858],[573,2775],{"className":2776,"style":854},[853],[573,2778,2780,2783],{"className":2779},[608],[573,2781],{"className":2782,"style":647},[612],[573,2784,1112],{"className":2785},[617],[809,2787,2788,2993],{},[812,2789,2790,2791,2842,2843,2894,2895,807],{},"Im 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= \\frac{2}{(1 + 4)^{3\u002F2}} = \\frac{2}{5^{3\u002F2}} \\approx 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der Krümmungsradius ist etwa ",[573,3405,3407,3422],{"className":3406},[576],[573,3408,3410],{"className":3409},[580],[582,3411,3412],{"xmlns":584},[586,3413,3414,3419],{},[589,3415,3416],{},[633,3417,3418],{},"5,59",[596,3420,3421],{"encoding":598},"5{,}59",[573,3423,3425],{"className":3424,"ariaHidden":604},[603],[573,3426,3428,3431,3434,3440],{"className":3427},[608],[573,3429],{"className":3430,"style":3389},[612],[573,3432,3100],{"className":3433},[617],[573,3435,3437],{"className":3436},[617],[573,3438,1456],{"className":3439},[1504],[573,3441,3443],{"className":3442},[617],"59",[564,3445,3446,3447,3512],{},"Die Parabel wird also nach außen hin immer flacher, obwohl ",[573,3448,3450,3471],{"className":3449},[576],[573,3451,3453],{"className":3452},[580],[582,3454,3455],{"xmlns":584},[586,3456,3457,3469],{},[589,3458,3459],{},[1100,3460,3461,3463],{},[592,3462,1104],{},[589,3464,3465,3467],{},[829,3466,1109],{"mathvariant":958},[829,3468,1109],{"mathvariant":958},[596,3470,1379],{"encoding":598},[573,3472,3474],{"className":3473,"ariaHidden":604},[603],[573,3475,3477,3480],{"className":3476},[608],[573,3478],{"className":3479,"style":1273},[612],[573,3481,3483,3486],{"className":3482},[617],[573,3484,1104],{"className":3485,"style":1171},[617,618],[573,3487,3489],{"className":3488},[1175],[573,3490,3492],{"className":3491},[731],[573,3493,3495],{"className":3494},[736],[573,3496,3498],{"className":3497,"style":1292},[740],[573,3499,3500,3503],{"style":1188},[573,3501],{"className":3502,"style":1192},[748],[573,3504,3506],{"className":3505},[753,754,755,756],[573,3507,3509],{"className":3508},[617,756],[573,3510,1421],{"className":3511},[617,756]," konstant ist.",[564,3514,3515,3516,3694,3695,3723,3724,3774,3775,1354,3874,4051,4052,4177,4178,4206],{},"Der obere Halbkreis ",[573,3517,3519,3556],{"className":3518},[576],[573,3520,3522],{"className":3521},[580],[582,3523,3524],{"xmlns":584},[586,3525,3526,3553],{},[589,3527,3528,3530,3532,3534,3536,3538],{},[592,3529,1104],{},[829,3531,1093],{"stretchy":1092},[592,3533,1446],{},[829,3535,1117],{"stretchy":1092},[829,3537,949],{},[3539,3540,3541],"msqrt",{},[589,3542,3543,3545,3547],{},[633,3544,3077],{},[829,3546,1575],{},[1100,3548,3549,3551],{},[592,3550,1446],{},[633,3552,1112],{},[596,3554,3555],{"encoding":598},"f(x) = \\sqrt{4 - 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0 400000 1080","xMinYMin slice",[3679,3680],"path",{"d":3681},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[573,3683,793],{"className":3684},[792],[573,3686,3688],{"className":3687},[736],[573,3689,3692],{"className":3690,"style":3691},[740],"height:0.1266em;",[573,3693],{}," mit Radius 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= -\\frac{1}{2}",[573,3916,3918,3974],{"className":3917,"ariaHidden":604},[603],[573,3919,3921,3924,3956,3959,3962,3965,3968,3971],{"className":3920},[608],[573,3922],{"className":3923,"style":2620},[612],[573,3925,3927,3930],{"className":3926},[617],[573,3928,1104],{"className":3929,"style":1171},[617,618],[573,3931,3933],{"className":3932},[1175],[573,3934,3936],{"className":3935},[731],[573,3937,3939],{"className":3938},[736],[573,3940,3942],{"className":3941,"style":1292},[740],[573,3943,3944,3947],{"style":1188},[573,3945],{"className":3946,"style":1192},[748],[573,3948,3950],{"className":3949},[753,754,755,756],[573,3951,3953],{"className":3952},[617,756],[573,3954,1421],{"className":3955},[617,756],[573,3957,1093],{"className":3958},[723],[573,3960,635],{"className":3961},[617],[573,3963,1117],{"className":3964},[806],[573,3966],{"className":3967,"style":854},[853],[573,3969,949],{"className":3970},[858],[573,3972],{"className":3973,"style":854},[853],[573,3975,3977,3980,3983],{"className":3976},[608],[573,3978],{"className":3979,"style":716},[612],[573,3981,1575],{"className":3982},[617],[573,3984,3986,3989,4048],{"className":3985},[617],[573,3987],{"className":3988},[723,724],[573,3990,3992],{"className":3991},[697],[573,3993,3995,4040],{"className":3994},[731,732],[573,3996,3998,4037],{"className":3997},[736],[573,3999,4001,4015,4023],{"className":4000,"style":741},[740],[573,4002,4003,4006],{"style":744},[573,4004],{"className":4005,"style":749},[748],[573,4007,4009],{"className":4008},[753,754,755,756],[573,4010,4012],{"className":4011},[617,756],[573,4013,1112],{"className":4014},[617,756],[573,4016,4017,4020],{"style":765},[573,4018],{"className":4019,"style":749},[748],[573,4021],{"className":4022,"style":773},[772],[573,4024,4025,4028],{"style":776},[573,4026],{"className":4027,"style":749},[748],[573,4029,4031],{"className":4030},[753,754,755,756],[573,4032,4034],{"className":4033},[617,756],[573,4035,701],{"className":4036},[617,756],[573,4038,793],{"className":4039},[792],[573,4041,4043],{"className":4042},[736],[573,4044,4046],{"className":4045,"style":800},[740],[573,4047],{},[573,4049],{"className":4050},[806,724],", also ",[573,4053,4055,4079],{"className":4054},[576],[573,4056,4058],{"className":4057},[580],[582,4059,4060],{"xmlns":584},[586,4061,4062,4076],{},[589,4063,4064,4066,4068,4070],{},[592,4065,594],{},[829,4067,949],{},[829,4069,1575],{},[697,4071,4072,4074],{},[633,4073,701],{},[633,4075,1112],{},[596,4077,4078],{"encoding":598},"\\kappa = -\\frac{1}{2}",[573,4080,4082,4100],{"className":4081,"ariaHidden":604},[603],[573,4083,4085,4088,4091,4094,4097],{"className":4084},[608],[573,4086],{"className":4087,"style":613},[612],[573,4089,594],{"className":4090},[617,618],[573,4092],{"className":4093,"style":854},[853],[573,4095,949],{"className":4096},[858],[573,4098],{"className":4099,"style":854},[853],[573,4101,4103,4106,4109],{"className":4102},[608],[573,4104],{"className":4105,"style":716},[612],[573,4107,1575],{"className":4108},[617],[573,4110,4112,4115,4174],{"className":4111},[617],[573,4113],{"className":4114},[723,724],[573,4116,4118],{"className":4117},[697],[573,4119,4121,4166],{"className":4120},[731,732],[573,4122,4124,4163],{"className":4123},[736],[573,4125,4127,4141,4149],{"className":4126,"style":741},[740],[573,4128,4129,4132],{"style":744},[573,4130],{"className":4131,"style":749},[748],[573,4133,4135],{"className":4134},[753,754,755,756],[573,4136,4138],{"className":4137},[617,756],[573,4139,1112],{"className":4140},[617,756],[573,4142,4143,4146],{"style":765},[573,4144],{"className":4145,"style":749},[748],[573,4147],{"className":4148,"style":773},[772],[573,4150,4151,4154],{"style":776},[573,4152],{"className":4153,"style":749},[748],[573,4155,4157],{"className":4156},[753,754,755,756],[573,4158,4160],{"className":4159},[617,756],[573,4161,701],{"className":4162},[617,756],[573,4164,793],{"className":4165},[792],[573,4167,4169],{"className":4168},[736],[573,4170,4172],{"className":4171,"style":800},[740],[573,4173],{},[573,4175],{"className":4176},[806,724],": eine Rechtskurve mit Radius ",[573,4179,4181,4194],{"className":4180},[576],[573,4182,4184],{"className":4183},[580],[582,4185,4186],{"xmlns":584},[586,4187,4188,4192],{},[589,4189,4190],{},[633,4191,1112],{},[596,4193,1112],{"encoding":598},[573,4195,4197],{"className":4196,"ariaHidden":604},[603],[573,4198,4200,4203],{"className":4199},[608],[573,4201],{"className":4202,"style":647},[612],[573,4204,1112],{"className":4205},[617],", wie erwartet.",[559,4208,4210],{"id":4209},"typische-fehler","Typische Fehler",[809,4212,4213,4281,4383],{},[812,4214,4215,4280],{},[573,4216,4218,4239],{"className":4217},[576],[573,4219,4221],{"className":4220},[580],[582,4222,4223],{"xmlns":584},[586,4224,4225,4237],{},[589,4226,4227],{},[1100,4228,4229,4231],{},[592,4230,1104],{},[589,4232,4233,4235],{},[829,4234,1109],{"mathvariant":958},[829,4236,1109],{"mathvariant":958},[596,4238,1379],{"encoding":598},[573,4240,4242],{"className":4241,"ariaHidden":604},[603],[573,4243,4245,4248],{"className":4244},[608],[573,4246],{"className":4247,"style":1273},[612],[573,4249,4251,4254],{"className":4250},[617],[573,4252,1104],{"className":4253,"style":1171},[617,618],[573,4255,4257],{"className":4256},[1175],[573,4258,4260],{"className":4259},[731],[573,4261,4263],{"className":4262},[736],[573,4264,4266],{"className":4265,"style":1292},[740],[573,4267,4268,4271],{"style":1188},[573,4269],{"className":4270,"style":1192},[748],[573,4272,4274],{"className":4273},[753,754,755,756],[573,4275,4277],{"className":4276},[617,756],[573,4278,1421],{"className":4279},[617,756]," mit der Krümmung gleichsetzen. Das stimmt nur an Stellen mit waagerechter Tangente.",[812,4282,4283,4284,4382],{},"Den Exponenten ",[573,4285,4287,4305],{"className":4286},[576],[573,4288,4290],{"className":4289},[580],[582,4291,4292],{"xmlns":584},[586,4293,4294,4302],{},[589,4295,4296],{},[697,4297,4298,4300],{},[633,4299,1122],{},[633,4301,1112],{},[596,4303,4304],{"encoding":598},"\\frac{3}{2}",[573,4306,4308],{"className":4307,"ariaHidden":604},[603],[573,4309,4311,4314],{"className":4310},[608],[573,4312],{"className":4313,"style":716},[612],[573,4315,4317,4320,4379],{"className":4316},[617],[573,4318],{"className":4319},[723,724],[573,4321,4323],{"className":4322},[697],[573,4324,4326,4371],{"className":4325},[731,732],[573,4327,4329,4368],{"className":4328},[736],[573,4330,4332,4346,4354],{"className":4331,"style":741},[740],[573,4333,4334,4337],{"style":744},[573,4335],{"className":4336,"style":749},[748],[573,4338,4340],{"className":4339},[753,754,755,756],[573,4341,4343],{"className":4342},[617,756],[573,4344,1112],{"className":4345},[617,756],[573,4347,4348,4351],{"style":765},[573,4349],{"className":4350,"style":749},[748],[573,4352],{"className":4353,"style":773},[772],[573,4355,4356,4359],{"style":776},[573,4357],{"className":4358,"style":749},[748],[573,4360,4362],{"className":4361},[753,754,755,756],[573,4363,4365],{"className":4364},[617,756],[573,4366,1122],{"className":4367},[617,756],[573,4369,793],{"className":4370},[792],[573,4372,4374],{"className":4373},[736],[573,4375,4377],{"className":4376,"style":800},[740],[573,4378],{},[573,4380],{"className":4381},[806,724]," im Nenner vergessen oder als Quadrat schreiben.",[812,4384,4385],{},"Das Vorzeichen falsch deuten. Es hängt von der Durchlaufrichtung ab; der Krümmungsradius verwendet deshalb den Betrag.",{"title":4387,"searchDepth":4388,"depth":4388,"links":4389},"",2,[4390,4391,4392],{"id":561,"depth":4388,"text":562},{"id":2477,"depth":4388,"text":2478},{"id":4209,"depth":4388,"text":4210},[4394,4397,4399,4402,4405,4408,4411],{"lhs":4395,"rhs":4396},"((-R*sin(t))*(-R*sin(t)) - (R*cos(t))*(-R*cos(t)))\u002F((R*sin(t))^2 + (R*cos(t))^2)^(3\u002F2)","1\u002FR",{"lhs":4398,"rhs":1112},"2\u002F(1 + (2*0)^2)^(3\u002F2)",{"lhs":4400,"rhs":4401},"2\u002F(1 + (2*1)^2)^(3\u002F2)","2\u002F5^(3\u002F2)",{"lhs":4403,"rhs":4404},"round(2\u002F5^(3\u002F2), 4)","0.1789",{"lhs":4406,"rhs":4407},"round(5^(3\u002F2)\u002F2, 2)","5.59",{"lhs":4409,"rhs":4410},"(-4\u002F(4 - 0^2)^(3\u002F2))\u002F(1 + 0^2)^(3\u002F2)","-0.5",{"lhs":4412,"rhs":635},"0\u002F(1 + m^2)^(3\u002F2)","f \\text{ zweimal differenzierbar}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">κ\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.7968em;vertical-align:-1.3679em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4289em;\">\u003Cspan style=\"top:-2.11em;\">\u003Cspan class=\"pstrut\" style=\"height:3.1279em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan 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