155:@0.918240:0.966765:0.943652:0.966765:0.943652:0.950778:0.918240:0.950778:0.000000:0.000000:0.000000 Competencia digital:@0.684804:0.718947:0.827156:0.718947:0.827156:0.703474:0.684804:0.703474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para conocer más sobre :@0.685042:0.747575:0.843262:0.747575:0.843262:0.732512:0.685042:0.732512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derivadas, :@0.638498:0.763417:0.706255:0.763417:0.706255:0.748354:0.638498:0.748354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 visita:@0.706255:0.763615:0.741046:0.763615:0.741046:0.748354:0.706255:0.748354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 esta página::@0.741048:0.763417:0.820291:0.763417:0.820291:0.748354:0.741048:0.748354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lynk.ec/12m09:@0.638498:0.786718:0.736387:0.786718:0.736387:0.771404:0.638498:0.771404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Luego, :@0.108233:0.103323:0.158342:0.103323:0.158342:0.086825:0.108233:0.086825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = lím ( ) = lím :@0.108233:0.127802:0.398618:0.127802:0.398618:0.111304:0.108233:0.111304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Q h:@0.199550:0.127918:0.226791:0.127918:0.226791:0.111449:0.199550:0.111449:0.000000:0.000000:0.000000 :@0.108233:0.162503:0.112375:0.162503:0.112375:0.146005:0.108233:0.146005:0.000000 = lím (6 + 6 – 36 + 6 + 2 + 3 ) = 6 + 6 – 36, .:@0.158497:0.162503:0.595767:0.162503:0.595767:0.146005:0.158497:0.146005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.213181:0.162619:0.220656:0.162619:0.220656:0.146150:0.213181:0.146150:0.000000 2:@0.220658:0.156151:0.225612:0.156151:0.225612:0.146533:0.220658:0.146533:0.000000 x:@0.251254:0.162619:0.258729:0.162619:0.258729:0.146150:0.251254:0.146150:0.000000 xh:@0.318201:0.162619:0.335039:0.162619:0.335039:0.146150:0.318201:0.146150:0.000000:0.000000 h:@0.360681:0.162619:0.370082:0.162619:0.370082:0.146150:0.360681:0.146150:0.000000 2:@0.370080:0.156151:0.375033:0.156151:0.375033:0.146533:0.370080:0.146533:0.000000 h:@0.400674:0.162619:0.410075:0.162619:0.410075:0.146150:0.400674:0.146150:0.000000 x:@0.442826:0.162619:0.450301:0.162619:0.450301:0.146150:0.442826:0.146150:0.000000 2:@0.450300:0.156151:0.455253:0.156151:0.455253:0.146533:0.450300:0.146533:0.000000 x:@0.482052:0.162619:0.489527:0.162619:0.489527:0.146150:0.482052:0.146150:0.000000 ∀:@0.538507:0.170089:0.550079:0.170089:0.550079:0.151090:0.538507:0.151090:0.000000 x:@0.550088:0.162619:0.557562:0.162619:0.557562:0.146150:0.550088:0.146150:0.000000 :@0.561308:0.161984:0.575961:0.161984:0.575961:0.148611:0.561308:0.148611:0.000000 :@0.579707:0.161416:0.593012:0.161416:0.593012:0.148554:0.579707:0.148554:0.000000 En primer lugar, determinamos los puntos en los que = 0.:@0.108241:0.189917:0.595743:0.189912:0.595743:0.173414:0.108241:0.173420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.401279:0.190033:0.408753:0.190033:0.408753:0.173564:0.401279:0.173564:0.000000 :@0.412406:0.189394:0.427059:0.189394:0.427059:0.176020:0.412406:0.176020:0.000000 :@0.430720:0.188825:0.444025:0.188825:0.444025:0.175963:0.430720:0.175963:0.000000 Se tiene :@0.108240:0.217326:0.172566:0.217326:0.172566:0.200829:0.108240:0.200829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = 0 :@0.112131:0.241805:0.183838:0.241805:0.183838:0.225308:0.112131:0.225308:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔ :@0.183838:0.241299:0.208729:0.241299:0.208729:0.223587:0.183838:0.223587:0.000000:0.000000 6 + 6 – 36 = 0 :@0.208729:0.241805:0.323543:0.241800:0.323543:0.225302:0.208729:0.225308:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.217225:0.241921:0.224700:0.241921:0.224700:0.225452:0.217225:0.225452:0.000000 2:@0.224692:0.235448:0.229646:0.235448:0.229646:0.225830:0.224692:0.225830:0.000000 x:@0.254342:0.241915:0.261817:0.241915:0.261817:0.225447:0.254342:0.225447:0.000000 ⇔:@0.323543:0.241294:0.343618:0.241294:0.343618:0.223581:0.323543:0.223581:0.000000 6( + 3)( – 2) = 0 :@0.343618:0.241800:0.471500:0.241800:0.471500:0.225302:0.343618:0.225302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.360764:0.241915:0.368239:0.241915:0.368239:0.225447:0.360764:0.225447:0.000000 x:@0.404843:0.241915:0.412318:0.241915:0.412318:0.225447:0.404843:0.225447:0.000000 ⇔ :@0.471500:0.241294:0.496391:0.241294:0.496391:0.223581:0.471500:0.223581:0.000000:0.000000 x:@0.496391:0.241915:0.503866:0.241915:0.503866:0.225447:0.496391:0.225447:0.000000 = –3 = 2.:@0.503866:0.241800:0.591876:0.241800:0.591876:0.225302:0.503866:0.225302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∨:@0.541755:0.248874:0.552133:0.248874:0.552133:0.230738:0.541755:0.230738:0.000000 x:@0.554829:0.241915:0.562303:0.241915:0.562303:0.225447:0.554829:0.225447:0.000000 La función es estrictamente creciente si y solo si, > 0.:@0.108241:0.269214:0.539449:0.269214:0.539449:0.252716:0.108241:0.252716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.187727:0.269330:0.196994:0.269330:0.196994:0.252861:0.187727:0.252861:0.000000 Entonces, > 0 :@0.108241:0.300821:0.257681:0.300821:0.257681:0.284324:0.108241:0.284324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.257681:0.300315:0.277756:0.300315:0.277756:0.282603:0.257681:0.282603:0.000000 6( + 3)( – 2) > 0 :@0.277756:0.300821:0.405638:0.300821:0.405638:0.284324:0.277756:0.284324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.294902:0.300937:0.302377:0.300937:0.302377:0.284468:0.294902:0.284468:0.000000 x:@0.338981:0.300937:0.346455:0.300937:0.346455:0.284468:0.338981:0.284468:0.000000 ⇔ :@0.405638:0.300315:0.430529:0.300315:0.430529:0.282603:0.405638:0.282603:0.000000:0.000000 x:@0.430529:0.300937:0.438004:0.300937:0.438004:0.284468:0.430529:0.284468:0.000000 ]–∞, –3[ ]2, ∞[,:@0.438004:0.300821:0.586960:0.300816:0.586960:0.284319:0.438004:0.284324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.440688:0.300298:0.455340:0.300298:0.455340:0.286924:0.440688:0.286924:0.000000 :@0.523596:0.300599:0.539644:0.300599:0.539644:0.285952:0.523596:0.285952:0.000000 y la función es estrictamente decreciente si y solo si < 0, luego:@0.108237:0.332423:0.592177:0.332423:0.592177:0.315926:0.108237:0.315926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 < 0 :@0.108237:0.364031:0.189671:0.364031:0.189671:0.347533:0.108237:0.347533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.189671:0.363525:0.209746:0.363525:0.209746:0.345812:0.189671:0.345812:0.000000 6( + 3)( – 2) < 0 :@0.209746:0.364031:0.337629:0.364031:0.337629:0.347533:0.209746:0.347533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.226892:0.364146:0.234367:0.364146:0.234367:0.347678:0.226892:0.347678:0.000000 x:@0.270971:0.364146:0.278446:0.364146:0.278446:0.347678:0.270971:0.347678:0.000000 ⇔ :@0.337629:0.363525:0.362519:0.363525:0.362519:0.345812:0.337629:0.345812:0.000000:0.000000 x:@0.362519:0.364146:0.369994:0.364146:0.369994:0.347678:0.362519:0.347678:0.000000 ]–3, 2[.:@0.369994:0.364031:0.435999:0.364029:0.435999:0.347532:0.369994:0.347533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.372683:0.363511:0.387336:0.363511:0.387336:0.350138:0.372683:0.350138:0.000000 Estos resultados se resumen a continuación::@0.108239:0.391444:0.419852:0.391444:0.419852:0.374946:0.108239:0.374946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.108239:0.416038:0.129932:0.416038:0.129932:0.399570:0.108239:0.399570:0.000000:0.000000:0.000000:0.000000 estrictamente creciente en el intervalo ]–∞, –3[ ]2, ∞[,:@0.129932:0.415923:0.538582:0.415923:0.538582:0.399425:0.129932:0.399425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.475219:0.415706:0.491267:0.415706:0.491267:0.401059:0.475219:0.401059:0.000000 p:@0.108239:0.433389:0.129932:0.433389:0.129932:0.416920:0.108239:0.416920:0.000000:0.000000:0.000000:0.000000 estrictamente decreciente en el intervalo ]–3, 2[.:@0.129932:0.433273:0.476529:0.433273:0.476529:0.416776:0.129932:0.416776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En el punto = –3, la función tiene un máximo local, mientras que :@0.108239:0.460688:0.599807:0.460688:0.599807:0.444190:0.108239:0.444190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.194586:0.460803:0.202061:0.460803:0.202061:0.444335:0.194586:0.444335:0.000000 p:@0.322158:0.460803:0.331425:0.460803:0.331425:0.444335:0.322158:0.444335:0.000000 en = 2, la función tiene un mínimo local.:@0.108239:0.478038:0.406791:0.478038:0.406791:0.461541:0.108239:0.461541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.129932:0.478154:0.137407:0.478154:0.137407:0.461685:0.129932:0.461685:0.000000 Por otro lado, (0) = 1, es decir que la gráfica de la función corta al :@0.108239:0.505453:0.599906:0.505453:0.599906:0.488955:0.108239:0.488955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.209227:0.505568:0.218494:0.505568:0.218494:0.489100:0.209227:0.489100:0.000000 p:@0.528761:0.505568:0.538028:0.505568:0.538028:0.489100:0.528761:0.489100:0.000000 eje en el punto (0, 1). Para hallar los puntos de corte de la gráfica de :@0.108239:0.522803:0.599906:0.522803:0.599906:0.506306:0.108239:0.506306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.132109:0.522919:0.139795:0.522919:0.139795:0.506450:0.132109:0.506450:0.000000 p :@0.108239:0.540270:0.121648:0.540270:0.121648:0.523801:0.108239:0.523801:0.000000:0.000000 con el eje , se debe resolver la ecuación en el conjunto ::@0.121648:0.540154:0.531939:0.540138:0.531939:0.523641:0.121648:0.523656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.192619:0.540270:0.200094:0.540270:0.200094:0.523801:0.192619:0.523801:0.000000 :@0.515879:0.539051:0.529184:0.539051:0.529184:0.526189:0.515879:0.526189:0.000000 p x:@0.228646:0.564733:0.251340:0.564733:0.251340:0.548264:0.228646:0.548264:0.000000:0.000000:0.000000 ( ) = 0 :@0.237913:0.564617:0.289023:0.564617:0.289023:0.548120:0.237913:0.548120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.289023:0.564111:0.309098:0.564111:0.309098:0.546399:0.289023:0.546399:0.000000 2 + 3 – 36 + 1 = 0,:@0.309098:0.564617:0.475357:0.564618:0.475357:0.548120:0.309098:0.548120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.321736:0.564733:0.329211:0.564733:0.329211:0.548264:0.321736:0.548264:0.000000 3:@0.329207:0.558265:0.334160:0.558265:0.334160:0.548647:0.329207:0.548647:0.000000 x:@0.361749:0.564734:0.369224:0.564734:0.369224:0.548265:0.361749:0.548265:0.000000 2:@0.369224:0.558265:0.374177:0.558265:0.374177:0.548647:0.369224:0.548647:0.000000 x:@0.409951:0.564734:0.417426:0.564734:0.417426:0.548265:0.409951:0.548265:0.000000 lo cual no es tarea fácil.:@0.108238:0.592032:0.271336:0.592032:0.271336:0.575535:0.108238:0.575535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La función no es par, pues (– ) ≠ ( ), ; tampoco es impar, :@0.108238:0.619446:0.599916:0.619436:0.599916:0.602939:0.108238:0.602949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.186455:0.619562:0.195722:0.619562:0.195722:0.603093:0.186455:0.603093:0.000000 p x:@0.305512:0.619562:0.338706:0.619562:0.338706:0.603093:0.305512:0.603093:0.000000:0.000000:0.000000 p x:@0.362480:0.619562:0.385174:0.619562:0.385174:0.603093:0.362480:0.603093:0.000000:0.000000:0.000000 ∀:@0.404360:0.627023:0.415933:0.627023:0.415933:0.608024:0.404360:0.608024:0.000000 x:@0.415939:0.619552:0.423414:0.619552:0.423414:0.603083:0.415939:0.603083:0.000000 :@0.426917:0.618918:0.441570:0.618918:0.441570:0.605544:0.426917:0.605544:0.000000 :@0.445073:0.618349:0.458378:0.618349:0.458378:0.605487:0.445073:0.605487:0.000000 ya que (– ) ≠ – ( ), .:@0.108232:0.636787:0.329861:0.636787:0.329861:0.620289:0.108232:0.620289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x:@0.159247:0.636903:0.192441:0.636903:0.192441:0.620434:0.159247:0.620434:0.000000:0.000000:0.000000 p x:@0.227985:0.636903:0.250680:0.636903:0.250680:0.620434:0.227985:0.620434:0.000000:0.000000:0.000000 ∀:@0.271810:0.644374:0.283383:0.644374:0.283383:0.625374:0.271810:0.625374:0.000000 x:@0.283391:0.636903:0.290866:0.636903:0.290866:0.620434:0.283391:0.620434:0.000000 :@0.295007:0.636268:0.309660:0.636268:0.309660:0.622895:0.295007:0.622895:0.000000 :@0.313802:0.635700:0.327106:0.635700:0.327106:0.622838:0.313802:0.622838:0.000000 Al emplear un programa para graficar, podemos apreciar los resulta-:@0.108234:0.664201:0.595782:0.664201:0.595782:0.647704:0.108234:0.647704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dos obtenidos:@0.108234:0.681552:0.209972:0.681552:0.209972:0.665054:0.108234:0.665054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dp a:@0.109981:0.120704:0.143271:0.120704:0.143271:0.104235:0.109981:0.104235:0.000000:0.000000:0.000000:0.000000 ( ):@0.128341:0.120588:0.149224:0.120588:0.149224:0.104091:0.128341:0.104091:0.000000:0.000000:0.000000 dx:@0.121347:0.137043:0.137839:0.137043:0.137839:0.120574:0.121347:0.120574:0.000000:0.000000 dp a:@0.525937:0.183628:0.559228:0.183628:0.559228:0.167159:0.525937:0.167159:0.000000:0.000000:0.000000:0.000000 ( ):@0.544297:0.183513:0.565181:0.183513:0.565181:0.167015:0.544297:0.167015:0.000000:0.000000:0.000000 dx:@0.537323:0.199967:0.553814:0.199967:0.553814:0.183498:0.537323:0.183498:0.000000:0.000000 dp x:@0.114571:0.234594:0.146359:0.234594:0.146359:0.218125:0.114571:0.218125:0.000000:0.000000:0.000000:0.000000 ( ):@0.132931:0.234478:0.152312:0.234478:0.152312:0.217981:0.132931:0.217981:0.000000:0.000000:0.000000 dx:@0.125186:0.250933:0.141677:0.250933:0.141677:0.234464:0.125186:0.234464:0.000000:0.000000 dp x:@0.114571:0.357195:0.146359:0.357195:0.146359:0.340726:0.114571:0.340726:0.000000:0.000000:0.000000:0.000000 ( ):@0.132931:0.357079:0.152312:0.357079:0.152312:0.340581:0.132931:0.340581:0.000000:0.000000:0.000000 dx:@0.125186:0.373533:0.141677:0.373533:0.141677:0.357065:0.125186:0.357065:0.000000:0.000000 dp x:@0.471144:0.262393:0.502931:0.262393:0.502931:0.245924:0.471144:0.245924:0.000000:0.000000:0.000000:0.000000 ( ):@0.489503:0.262277:0.508884:0.262277:0.508884:0.245780:0.489503:0.245780:0.000000:0.000000:0.000000 dx:@0.481759:0.278732:0.498250:0.278732:0.498250:0.262263:0.481759:0.262263:0.000000:0.000000 dp x:@0.478742:0.325833:0.510530:0.325833:0.510530:0.309364:0.478742:0.309364:0.000000:0.000000:0.000000:0.000000 ( ):@0.497102:0.325717:0.516483:0.325717:0.516483:0.309219:0.497102:0.309219:0.000000:0.000000:0.000000 dx:@0.489358:0.342171:0.505849:0.342171:0.505849:0.325703:0.489358:0.325703:0.000000:0.000000 dp x:@0.185522:0.293756:0.217310:0.293756:0.217310:0.277288:0.185522:0.277288:0.000000:0.000000:0.000000:0.000000 ( ):@0.203882:0.293641:0.223263:0.293641:0.223263:0.277143:0.203882:0.277143:0.000000:0.000000:0.000000 dx:@0.196137:0.310095:0.212628:0.310095:0.212628:0.293626:0.196137:0.293626:0.000000:0.000000 h:@0.172562:0.135726:0.178694:0.135726:0.178694:0.124986:0.172562:0.124986:0.000000 →:@0.178694:0.135044:0.189441:0.135044:0.189441:0.125033:0.178694:0.125033:0.000000 0:@0.189440:0.135651:0.194981:0.135651:0.194981:0.124891:0.189440:0.124891:0.000000 h:@0.253066:0.135726:0.259197:0.135726:0.259197:0.124986:0.253066:0.124986:0.000000 →:@0.259197:0.135044:0.269945:0.135044:0.269945:0.125033:0.259197:0.125033:0.000000 0:@0.269944:0.135651:0.275485:0.135651:0.275485:0.124891:0.269944:0.124891:0.000000 p a + h:@0.285008:0.120696:0.337775:0.120696:0.337775:0.104228:0.285008:0.104228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.294274:0.120581:0.300227:0.120581:0.300227:0.104083:0.294274:0.104083:0.000000 ) – ( ):@0.337775:0.120581:0.392662:0.120581:0.392662:0.104083:0.337775:0.104083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p a:@0.362512:0.120696:0.386709:0.120696:0.386709:0.104228:0.362512:0.104228:0.000000:0.000000:0.000000 h:@0.334134:0.137035:0.343536:0.137035:0.343536:0.120566:0.334134:0.120566:0.000000 Interdisciplinariedad:@0.684408:0.111444:0.831193:0.111444:0.831193:0.095972:0.684408:0.095972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática e Historia:@0.684646:0.140494:0.840314:0.140494:0.840314:0.125022:0.684646:0.125022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A través de la historia se re-:@0.638103:0.155913:0.815074:0.155913:0.815074:0.140850:0.638103:0.140850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conoce que, a finales del siglo :@0.638103:0.171755:0.832663:0.171755:0.832663:0.156692:0.638103:0.156692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 XVII y principios del XVIII, se :@0.638103:0.187597:0.825785:0.187597:0.825785:0.172534:0.638103:0.172534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dio origen al cálculo :@0.638103:0.203439:0.771873:0.203439:0.771873:0.188376:0.638103:0.188376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diferencial:@0.771873:0.203637:0.841583:0.203637:0.841583:0.188376:0.771873:0.188376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.841584:0.203439:0.845366:0.203439:0.845366:0.188376:0.841584:0.188376:0.000000 a partir de algunos problemas, :@0.638103:0.219281:0.837588:0.219281:0.837588:0.204218:0.638103:0.204218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 por ejemplo, el trazado de la :@0.638103:0.235123:0.826471:0.235123:0.826471:0.220060:0.638103:0.220060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tangente a una curva y las con-:@0.638103:0.250965:0.839788:0.250965:0.839788:0.235902:0.638103:0.235902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diciones para obtener máximos :@0.638103:0.266807:0.846524:0.266807:0.846524:0.251744:0.638103:0.251744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y mínimos, la velocidad de los :@0.638103:0.282649:0.835776:0.282649:0.835776:0.267586:0.638103:0.267586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cuerpos en movimiento, entre :@0.638103:0.298491:0.837275:0.298491:0.837275:0.283428:0.638103:0.283428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 otros.:@0.638103:0.314333:0.674321:0.314333:0.674321:0.299270:0.638103:0.299270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Indaga escribe:@0.638108:0.454101:0.750241:0.454101:0.750241:0.438629:0.638108:0.438629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.685740:0.453679:0.700445:0.453679:0.700445:0.438616:0.685740:0.438616:0.000000:0.000000:0.000000 otras aplica-:@0.750244:0.453679:0.832845:0.453679:0.832845:0.438616:0.750244:0.438616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ciones del cálculo diferencial en :@0.638108:0.469521:0.846124:0.469521:0.846124:0.454458:0.638108:0.454458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la vida cotidiana.:@0.638108:0.485363:0.746076:0.485363:0.746076:0.470300:0.638108:0.470300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Flavio Muñoz M. Colección Rally:@0.871305:0.427480:0.871305:0.336442:0.859836:0.336442:0.859836:0.427480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Glosario:@0.685849:0.568274:0.753314:0.568274:0.753314:0.550591:0.685849:0.550591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diferencial. :@0.686087:0.595087:0.762586:0.595087:0.762586:0.579826:0.686087:0.579826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Diferencia :@0.762586:0.594889:0.831396:0.594889:0.831396:0.579826:0.762586:0.579826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 infinitamente pequeña de una :@0.639544:0.610731:0.840351:0.610731:0.840351:0.595668:0.639544:0.595668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 variable.:@0.639544:0.626573:0.692067:0.626573:0.692067:0.611510:0.639544:0.611510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.633115:0.572005:0.644520:0.570496:0.639317:0.548351:0.627912:0.549860:0.000000 c:@0.636497:0.582975:0.647096:0.581572:0.642013:0.559937:0.631414:0.561340:0.000000 b:@0.646872:0.575757:0.659586:0.574074:0.654454:0.552232:0.641740:0.553914:0.000000 -20:@0.329239:0.869886:0.342959:0.869886:0.342959:0.859844:0.329239:0.859844:0.000000:0.000000:0.000000 20:@0.330928:0.820891:0.341271:0.820891:0.341271:0.810848:0.330928:0.810848:0.000000:0.000000 -60:@0.329239:0.918213:0.342959:0.918213:0.342959:0.908171:0.329239:0.908171:0.000000:0.000000:0.000000 80:@0.330928:0.747252:0.341271:0.747252:0.341271:0.737210:0.330928:0.737210:0.000000:0.000000 60:@0.330928:0.771895:0.341271:0.771895:0.341271:0.761853:0.330928:0.761853:0.000000:0.000000 40:@0.330928:0.796397:0.341271:0.796397:0.341271:0.786355:0.330928:0.786355:0.000000:0.000000 -40:@0.329239:0.893720:0.342959:0.893720:0.342959:0.883678:0.329239:0.883678:0.000000:0.000000:0.000000 100:@0.328336:0.722609:0.343850:0.722609:0.343850:0.712567:0.328336:0.712567:0.000000:0.000000:0.000000 y:@0.359599:0.705975:0.364360:0.705975:0.364360:0.695932:0.359599:0.695932:0.000000 x:@0.577059:0.838053:0.581926:0.838053:0.581926:0.828011:0.577059:0.828011:0.000000 4:@0.477628:0.852355:0.482800:0.852355:0.482800:0.842312:0.477628:0.842312:0.000000 0:@0.337940:0.852355:0.343112:0.852355:0.343112:0.842312:0.337940:0.842312:0.000000 2:@0.412569:0.852355:0.417740:0.852355:0.417740:0.842312:0.412569:0.842312:0.000000 6:@0.542782:0.852355:0.547953:0.852355:0.547953:0.842312:0.542782:0.842312:0.000000 –2:@0.279072:0.852355:0.290635:0.852355:0.290635:0.842312:0.279072:0.842312:0.000000:0.000000 –4:@0.214013:0.852355:0.225575:0.852355:0.225575:0.842312:0.214013:0.842312:0.000000:0.000000 –6:@0.148836:0.852355:0.160398:0.852355:0.160398:0.842312:0.148836:0.842312:0.000000:0.000000 (2 , 43):@0.389032:0.906191:0.440060:0.906191:0.440060:0.891845:0.389032:0.891845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – :@0.411195:0.905229:0.420107:0.905229:0.420107:0.895187:0.411195:0.895187:0.000000:0.000000 ( 3 , 82):@0.227036:0.735713:0.275539:0.735712:0.275539:0.721366:0.227036:0.721368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.232209:0.734750:0.238600:0.734750:0.238600:0.724708:0.232209:0.724708:0.000000 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000 maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000 ®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000