39:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento espacial, numérico y variacional:@0.522009:0.043661:0.926913:0.043661:0.926913:0.024916:0.522009:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 EBC 11. Comprende los conceptos de dominio y rango de una función y desarrolla herramientas para hallarlos.:@0.080927:0.971338:0.662716:0.971338:0.662716:0.959911:0.080927:0.959911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejemplo 3:@0.073089:0.136836:0.148872:0.136836:0.148872:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : graficar las funciones polinómicas. :@0.148761:0.136836:0.407589:0.136836:0.407589:0.121124:0.148761:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. :@0.104633:0.164199:0.120077:0.164199:0.120077:0.148487:0.104633:0.148487:0.000000:0.000000:0.000000 y:@0.134834:0.164199:0.142307:0.164199:0.142307:0.148764:0.134834:0.148764:0.000000 2 :@0.142234:0.164199:0.221507:0.164199:0.221507:0.148487:0.142234:0.148487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.146191:0.163645:0.161524:0.163645:0.161524:0.149929:0.146191:0.149929:0.000000 x:@0.174281:0.164199:0.181736:0.164199:0.181736:0.148764:0.174281:0.148764:0.000000 4:@0.181675:0.158135:0.186912:0.158135:0.186912:0.148975:0.181675:0.148975:0.000000 2:@0.190822:0.163645:0.206155:0.163645:0.206155:0.149929:0.190822:0.149929:0.000000 x:@0.210021:0.164199:0.217476:0.164199:0.217476:0.148764:0.210021:0.148764:0.000000 0:@0.231301:0.281077:0.239467:0.281077:0.239467:0.266793:0.231301:0.266793:0.000000 5:@0.329747:0.284014:0.337913:0.284014:0.337913:0.269730:0.329747:0.269730:0.000000 Sube a la :@0.261573:0.294869:0.325312:0.294869:0.325312:0.280585:0.261573:0.280585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derecha:@0.266391:0.309988:0.320508:0.309988:0.320508:0.295704:0.266391:0.295704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sube a la :@0.163114:0.294859:0.226854:0.294859:0.226854:0.280575:0.163114:0.280575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 izquierda:@0.164419:0.309988:0.225548:0.309988:0.225548:0.295704:0.164419:0.295704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.229051:0.208206:0.237217:0.208206:0.237217:0.193921:0.229051:0.193921:0.000000 2:@0.141683:0.281985:0.155622:0.281985:0.155622:0.269516:0.141683:0.269516:0.000000 5:@0.155622:0.282489:0.163789:0.282489:0.163789:0.268205:0.155622:0.268205:0.000000 Figura 4.2:@0.160368:0.324881:0.211694:0.324881:0.211694:0.313454:0.160368:0.313454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. :@0.545774:0.162299:0.561218:0.162299:0.561218:0.146587:0.545774:0.146587:0.000000:0.000000:0.000000 y:@0.575976:0.162299:0.583449:0.162299:0.583449:0.146864:0.575976:0.146864:0.000000 4 4:@0.583375:0.162299:0.660145:0.162299:0.660145:0.146587:0.583375:0.146587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.587333:0.161745:0.602666:0.161745:0.602666:0.148029:0.587333:0.148029:0.000000 x:@0.615422:0.162299:0.622877:0.162299:0.622877:0.146864:0.615422:0.146864:0.000000 4:@0.622817:0.156236:0.628054:0.156236:0.628054:0.147075:0.622817:0.147075:0.000000 1:@0.631964:0.161745:0.647297:0.161745:0.647297:0.148029:0.631964:0.148029:0.000000 x :@0.660053:0.162299:0.689247:0.162299:0.689247:0.146864:0.660053:0.146864:0.000000:0.000000:0.000000:0.000000 1:@0.670693:0.161745:0.686026:0.161745:0.686026:0.148029:0.670693:0.148029:0.000000 5:@0.689173:0.162299:0.698156:0.162299:0.698156:0.146587:0.689173:0.146587:0.000000 0:@0.672443:0.279177:0.680609:0.279177:0.680609:0.264893:0.672443:0.264893:0.000000 5:@0.770888:0.282114:0.779054:0.282114:0.779054:0.267830:0.770888:0.267830:0.000000 Baja a la :@0.726226:0.227625:0.783188:0.227625:0.783188:0.213341:0.726226:0.213341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derecha:@0.727648:0.242754:0.781765:0.242754:0.781765:0.228470:0.727648:0.228470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Baja a la :@0.599115:0.227625:0.656077:0.227625:0.656077:0.213341:0.599115:0.213341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 izquierda:@0.597023:0.242754:0.658152:0.242754:0.658152:0.228470:0.597023:0.228470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.670184:0.206306:0.678350:0.206306:0.678350:0.192022:0.670184:0.192022:0.000000 2:@0.582816:0.280085:0.596756:0.280085:0.596756:0.267616:0.582816:0.267616:0.000000 5:@0.596756:0.280589:0.604922:0.280589:0.604922:0.266305:0.596756:0.266305:0.000000 Figura 4.3:@0.603407:0.324881:0.654733:0.324881:0.654733:0.313454:0.603407:0.313454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. :@0.104633:0.366897:0.120077:0.366897:0.120077:0.351184:0.104633:0.351184:0.000000:0.000000:0.000000 y:@0.134834:0.366897:0.142307:0.366897:0.142307:0.351462:0.134834:0.351462:0.000000 :@0.142234:0.366897:0.201192:0.366897:0.201192:0.351184:0.142234:0.351184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.146191:0.366342:0.161524:0.366342:0.161524:0.352627:0.146191:0.352627:0.000000 x:@0.165390:0.366897:0.172845:0.366897:0.172845:0.351462:0.165390:0.351462:0.000000 3:@0.172773:0.360833:0.178010:0.360833:0.178010:0.351673:0.172773:0.351673:0.000000 2 1:@0.181920:0.366342:0.227091:0.366342:0.227091:0.352627:0.181920:0.352627:0.000000:0.000000:0.000000 x :@0.201118:0.366897:0.230312:0.366897:0.230312:0.351462:0.201118:0.351462:0.000000:0.000000:0.000000:0.000000 2:@0.230239:0.366897:0.239222:0.366897:0.239222:0.351184:0.230239:0.351184:0.000000 0:@0.229849:0.482153:0.237894:0.482153:0.237894:0.468081:0.229849:0.468081:0.000000 5:@0.326829:0.485047:0.334874:0.485047:0.334874:0.470975:0.326829:0.470975:0.000000 Sube a la :@0.279501:0.431368:0.342292:0.431368:0.342292:0.417296:0.279501:0.417296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derecha:@0.284232:0.446272:0.337545:0.446272:0.337545:0.432200:0.284232:0.432200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Baja a la :@0.157612:0.431368:0.213727:0.431368:0.213727:0.417296:0.157612:0.417296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 izquierda:@0.155552:0.446272:0.215771:0.446272:0.215771:0.432200:0.155552:0.432200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.227623:0.410366:0.235668:0.410366:0.235668:0.396294:0.227623:0.396294:0.000000 2:@0.141556:0.483047:0.155288:0.483047:0.155288:0.470764:0.141556:0.470764:0.000000 5:@0.155288:0.483544:0.163332:0.483544:0.163332:0.469472:0.155288:0.469472:0.000000 Figura 4.4:@0.160368:0.527155:0.211694:0.527155:0.211694:0.515728:0.160368:0.515728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. :@0.545774:0.368605:0.561218:0.368605:0.561218:0.352893:0.545774:0.352893:0.000000:0.000000:0.000000 y:@0.575976:0.368605:0.583449:0.368605:0.583449:0.353170:0.575976:0.353170:0.000000 :@0.583375:0.368605:0.606605:0.368605:0.606605:0.352893:0.583375:0.352893:0.000000:0.000000:0.000000 5 2 1:@0.587333:0.368051:0.653636:0.368051:0.653636:0.354335:0.587333:0.354335:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.621773:0.368605:0.629228:0.368605:0.629228:0.353170:0.621773:0.353170:0.000000 5:@0.629156:0.362541:0.634393:0.362541:0.634393:0.353381:0.629156:0.353381:0.000000 :@0.634345:0.368605:0.657575:0.368605:0.657575:0.352893:0.634345:0.352893:0.000000:0.000000:0.000000 x x:@0.657501:0.368605:0.708151:0.368605:0.708151:0.353170:0.657501:0.353170:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4:@0.664876:0.362541:0.670113:0.362541:0.670113:0.353381:0.664876:0.353381:0.000000 1:@0.673306:0.368051:0.688640:0.368051:0.688640:0.354335:0.673306:0.354335:0.000000 3:@0.691787:0.368605:0.700770:0.368605:0.700770:0.352893:0.691787:0.352893:0.000000 3 :@0.708093:0.362541:0.715637:0.362541:0.715637:0.353381:0.708093:0.353381:0.000000:0.000000 2:@0.715586:0.368051:0.730919:0.368051:0.730919:0.354335:0.715586:0.354335:0.000000 1.:@0.730827:0.368605:0.746879:0.368605:0.746879:0.352893:0.730827:0.352893:0.000000:0.000000:0.000000 0:@0.672329:0.505553:0.680486:0.505553:0.680486:0.490630:0.672329:0.490630:0.000000 5:@0.770659:0.508487:0.778816:0.508487:0.778816:0.493564:0.770659:0.493564:0.000000 Baja a la :@0.726049:0.454061:0.782944:0.454061:0.782944:0.439139:0.726049:0.439139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derecha:@0.727470:0.469172:0.781524:0.469172:0.781524:0.454250:0.727470:0.454250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sube a la :@0.590680:0.454061:0.654345:0.454061:0.654345:0.439139:0.590680:0.439139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 izquierda:@0.591983:0.469172:0.653041:0.469172:0.653041:0.454250:0.591983:0.454250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.670073:0.432767:0.678229:0.432767:0.678229:0.417844:0.670073:0.417844:0.000000 2:@0.582807:0.506459:0.596730:0.506459:0.596730:0.494005:0.582807:0.494005:0.000000 5:@0.596730:0.506963:0.604887:0.506963:0.604887:0.492041:0.596730:0.492041:0.000000 Figura 4.5:@0.603407:0.550028:0.654733:0.550028:0.654733:0.538600:0.603407:0.538600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Funciones polinómicas::@0.073089:0.588918:0.250936:0.588918:0.250936:0.572248:0.073089:0.572248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ceros de la función (cortes con el eje ); corte con el eje ; máximos y mínimos locales.:@0.250774:0.588918:0.874791:0.588918:0.874791:0.573205:0.250774:0.573205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.522815:0.588918:0.530270:0.588918:0.530270:0.573483:0.522815:0.573483:0.000000 y:@0.657722:0.588918:0.665195:0.588918:0.665195:0.573483:0.657722:0.573483:0.000000 Consideremos la función polinómica :@0.073089:0.619137:0.343642:0.619137:0.343642:0.603424:0.073089:0.603424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.073089:0.649356:0.080562:0.649356:0.080562:0.633920:0.073089:0.633920:0.000000 5:@0.080489:0.649356:0.148355:0.649362:0.148355:0.633649:0.080489:0.633643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.084446:0.648801:0.099779:0.648801:0.099779:0.635085:0.084446:0.635085:0.000000 x:@0.103645:0.649356:0.111100:0.649356:0.111100:0.633920:0.103645:0.633920:0.000000 3:@0.111026:0.643298:0.116263:0.643298:0.116263:0.634137:0.111026:0.634137:0.000000 2:@0.120174:0.648807:0.135507:0.648807:0.135507:0.635091:0.120174:0.635091:0.000000 x x:@0.148263:0.649362:0.207814:0.649362:0.207814:0.633927:0.148263:0.633927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.155649:0.643298:0.160886:0.643298:0.160886:0.634137:0.155649:0.634137:0.000000 2:@0.164078:0.648807:0.179411:0.648807:0.179411:0.635091:0.164078:0.635091:0.000000 29:@0.182559:0.649362:0.200451:0.649362:0.200451:0.633649:0.182559:0.633649:0.000000:0.000000 :@0.207767:0.643298:0.210117:0.643298:0.210117:0.634137:0.207767:0.634137:0.000000 1:@0.210069:0.648807:0.225403:0.648807:0.225403:0.635091:0.210069:0.635091:0.000000 105:@0.225311:0.649362:0.256069:0.649362:0.256069:0.633649:0.225311:0.633649:0.000000:0.000000:0.000000:0.000000 .:@0.255967:0.649047:0.258879:0.649047:0.258879:0.634762:0.255967:0.634762:0.000000 Se llama:@0.073089:0.679584:0.133752:0.679584:0.133752:0.663872:0.073089:0.663872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cero de una función:@0.133630:0.679584:0.288573:0.679584:0.288573:0.662915:0.133630:0.662915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 al valor que puede tomar para que 0.:@0.288417:0.679584:0.614722:0.679584:0.614722:0.663872:0.288417:0.663872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.347762:0.679584:0.357021:0.679584:0.357021:0.664149:0.347762:0.664149:0.000000 x:@0.492406:0.679584:0.499861:0.679584:0.499861:0.664149:0.492406:0.664149:0.000000 y:@0.572054:0.679584:0.579528:0.679584:0.579528:0.664149:0.572054:0.664149:0.000000 5:@0.583412:0.679030:0.598745:0.679030:0.598745:0.665314:0.583412:0.665314:0.000000 Un forma de obtener los ceros de la función es factorizar el polinomio 5:@0.073070:0.709803:0.626060:0.709806:0.626060:0.694093:0.073070:0.694091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.581332:0.709803:0.588786:0.709803:0.588786:0.694368:0.581332:0.694368:0.000000 3:@0.588730:0.703742:0.593967:0.703742:0.593967:0.694581:0.588730:0.694581:0.000000 2:@0.597878:0.709251:0.613212:0.709251:0.613212:0.695535:0.597878:0.695535:0.000000 x x:@0.625968:0.709806:0.685519:0.709806:0.685519:0.694370:0.625968:0.694370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.633353:0.703742:0.638589:0.703742:0.638589:0.694581:0.633353:0.694581:0.000000 2:@0.641783:0.709251:0.657116:0.709251:0.657116:0.695535:0.641783:0.695535:0.000000 29:@0.660264:0.709806:0.678156:0.709806:0.678156:0.694093:0.660264:0.694093:0.000000:0.000000 :@0.685470:0.703742:0.687820:0.703742:0.687820:0.694581:0.685470:0.694581:0.000000 1:@0.687773:0.709251:0.703106:0.709251:0.703106:0.695535:0.687773:0.695535:0.000000 105.:@0.703014:0.709806:0.736902:0.709806:0.736902:0.694093:0.703014:0.694093:0.000000:0.000000:0.000000:0.000000:0.000000 Al factorizar el polinomio, obtenemos:@0.073081:0.740025:0.345521:0.740025:0.345521:0.724312:0.073081:0.724312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.073081:0.770243:0.080554:0.770243:0.080554:0.754808:0.073081:0.754808:0.000000 ( 5) (:@0.080481:0.770243:0.161509:0.770243:0.161509:0.754531:0.080481:0.754531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.084438:0.769689:0.099771:0.769689:0.099771:0.755973:0.084438:0.755973:0.000000 x:@0.108423:0.770243:0.115878:0.770243:0.115878:0.754808:0.108423:0.754808:0.000000 1:@0.119762:0.769689:0.135095:0.769689:0.135095:0.755973:0.119762:0.755973:0.000000 x :@0.161399:0.770243:0.190593:0.770243:0.190593:0.754808:0.161399:0.754808:0.000000:0.000000:0.000000:0.000000 2:@0.172038:0.769689:0.187372:0.769689:0.187372:0.755973:0.172038:0.755973:0.000000 3)(:@0.190519:0.770243:0.209111:0.770243:0.209111:0.754531:0.190519:0.754531:0.000000:0.000000:0.000000 x:@0.209019:0.770243:0.216473:0.770243:0.216473:0.754808:0.209019:0.754808:0.000000 :@0.216422:0.764187:0.218772:0.764187:0.218772:0.755027:0.216422:0.755027:0.000000 2:@0.218724:0.769696:0.234057:0.769696:0.234057:0.755981:0.218724:0.755981:0.000000 7) :@0.233965:0.770251:0.258557:0.770251:0.258557:0.754538:0.233965:0.754538:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.251615:0.769936:0.254526:0.769936:0.254526:0.755651:0.251615:0.755651:0.000000 Por lo tanto, ( 5) (:@0.073086:0.800470:0.221761:0.800470:0.221761:0.784757:0.073086:0.784757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.168675:0.800470:0.176130:0.800470:0.176130:0.785034:0.168675:0.785034:0.000000 1:@0.180014:0.799915:0.195347:0.799915:0.195347:0.786199:0.180014:0.786199:0.000000 x :@0.221651:0.800470:0.250845:0.800470:0.250845:0.785034:0.221651:0.785034:0.000000:0.000000:0.000000:0.000000 2:@0.232290:0.799915:0.247624:0.799915:0.247624:0.786199:0.232290:0.786199:0.000000 3)(:@0.250771:0.800470:0.269363:0.800470:0.269363:0.784757:0.250771:0.784757:0.000000:0.000000:0.000000 x:@0.269271:0.800470:0.276725:0.800470:0.276725:0.785034:0.269271:0.785034:0.000000 :@0.276669:0.794408:0.279019:0.794408:0.279019:0.785248:0.276669:0.785248:0.000000 2:@0.278973:0.799917:0.294306:0.799917:0.294306:0.786202:0.278973:0.786202:0.000000 7) 0:@0.294214:0.800472:0.343987:0.800472:0.343987:0.784760:0.294214:0.784760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.315806:0.799917:0.331139:0.799917:0.331139:0.786202:0.315806:0.786202:0.000000 , lo que:@0.343907:0.800157:0.392201:0.800157:0.392201:0.785873:0.343907:0.785873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 implica::@0.392082:0.800472:0.452126:0.800472:0.452126:0.784760:0.392082:0.784760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.073084:0.830691:0.080539:0.830691:0.080539:0.815256:0.073084:0.815256:0.000000 5 0:@0.080466:0.830691:0.144652:0.830691:0.144652:0.814978:0.080466:0.814978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 5:@0.084423:0.830136:0.131803:0.830136:0.131803:0.816421:0.084423:0.816421:0.000000:0.000000:0.000000 :@0.144565:0.830380:0.169816:0.830380:0.169816:0.816095:0.144565:0.816095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.169704:0.830695:0.198898:0.830695:0.198898:0.815260:0.169704:0.815260:0.000000:0.000000:0.000000:0.000000 2 5:@0.180343:0.830140:0.226654:0.830140:0.226654:0.816424:0.180343:0.816424:0.000000:0.000000:0.000000 3:@0.198824:0.830695:0.207807:0.830695:0.207807:0.814982:0.198824:0.814982:0.000000 :@0.207730:0.830380:0.211395:0.830380:0.211395:0.816095:0.207730:0.816095:0.000000 0 :@0.226562:0.830695:0.259290:0.830695:0.259290:0.814982:0.226562:0.814982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.259167:0.830380:0.262831:0.830380:0.262831:0.816095:0.259167:0.816095:0.000000 x:@0.262759:0.830695:0.270214:0.830695:0.270214:0.815260:0.262759:0.815260:0.000000 :@0.270147:0.824631:0.272497:0.824631:0.272497:0.815470:0.270147:0.815470:0.000000 2 5:@0.272450:0.830140:0.319469:0.830140:0.319469:0.816424:0.272450:0.816424:0.000000:0.000000:0.000000 7:@0.287691:0.830695:0.300631:0.830695:0.300631:0.814982:0.287691:0.814982:0.000000:0.000000 :@0.300544:0.830380:0.304209:0.830380:0.304209:0.816095:0.300544:0.816095:0.000000 0 con lo cual concluimos::@0.319377:0.830695:0.509478:0.830695:0.509478:0.814982:0.319377:0.814982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.332228:0.830380:0.338738:0.830380:0.338738:0.816095:0.332228:0.816095:0.000000:0.000000 Los ceros de la función son :@0.073098:0.860914:0.283588:0.860917:0.283588:0.845205:0.073098:0.845201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.268584:0.860602:0.272249:0.860602:0.272249:0.846318:0.268584:0.846318:0.000000 x:@0.272176:0.860917:0.279630:0.860917:0.279630:0.845482:0.272176:0.845482:0.000000 5:@0.283514:0.860363:0.298848:0.860363:0.298848:0.846647:0.283514:0.846647:0.000000 :@0.298756:0.860602:0.302420:0.860602:0.302420:0.846318:0.298756:0.846318:0.000000 2:@0.302353:0.860098:0.316293:0.860098:0.316293:0.847629:0.302353:0.847629:0.000000 5, :@0.316204:0.860917:0.343594:0.860917:0.343594:0.845205:0.316204:0.845205:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.332181:0.860917:0.339636:0.860917:0.339636:0.845482:0.332181:0.845482:0.000000 5:@0.343520:0.860363:0.358854:0.860363:0.358854:0.846647:0.343520:0.846647:0.000000 :@0.358758:0.860602:0.362423:0.860602:0.362423:0.846318:0.358758:0.846318:0.000000 3 y :@0.362349:0.860917:0.398575:0.860917:0.398575:0.845205:0.362349:0.845205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.387162:0.860917:0.394617:0.860917:0.394617:0.845482:0.387162:0.845482:0.000000 5:@0.398501:0.860363:0.413834:0.860363:0.413834:0.846647:0.398501:0.846647:0.000000 :@0.413751:0.860602:0.433112:0.860602:0.433112:0.846318:0.413751:0.846318:0.000000:0.000000:0.000000 7.:@0.417342:0.860917:0.429454:0.860917:0.429454:0.845205:0.417342:0.845205:0.000000:0.000000 Los puntos de corte con el eje son:@0.073089:0.891139:0.332999:0.891139:0.332999:0.875426:0.073089:0.875426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.295283:0.891139:0.302738:0.891139:0.302738:0.875703:0.295283:0.875703:0.000000 (:@0.332904:0.890824:0.340937:0.890824:0.340937:0.876539:0.332904:0.876539:0.000000:0.000000 2:@0.340853:0.890319:0.354792:0.890319:0.354792:0.877850:0.340853:0.877850:0.000000 5, 0), (3, 0) y (7, 0):@0.354712:0.891139:0.476550:0.891139:0.476550:0.875426:0.354712:0.875426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . :@0.476320:0.890824:0.486561:0.890824:0.486561:0.876539:0.476320:0.876539:0.000000:0.000000:0.000000 La intersección en el eje es 105 valor que toma cuando 0 o lo que es lo mismo, el punto de corte con el eje :@0.073089:0.921361:0.931067:0.921361:0.931067:0.905648:0.073089:0.905648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.249596:0.921361:0.257070:0.921361:0.257070:0.905926:0.249596:0.905926:0.000000 y:@0.280152:0.921361:0.287626:0.921361:0.287626:0.905926:0.280152:0.905926:0.000000 5:@0.291307:0.920806:0.306640:0.920806:0.306640:0.907091:0.291307:0.907091:0.000000 (:@0.337041:0.921046:0.344889:0.921046:0.344889:0.906762:0.337041:0.906762:0.000000:0.000000 y:@0.458433:0.921361:0.465907:0.921361:0.465907:0.905926:0.458433:0.905926:0.000000 x:@0.528896:0.921361:0.536351:0.921361:0.536351:0.905926:0.528896:0.905926:0.000000 5:@0.540033:0.920806:0.555366:0.920806:0.555366:0.907091:0.540033:0.907091:0.000000 y:@0.073078:0.938003:0.080551:0.938003:0.080551:0.922568:0.073078:0.922568:0.000000 es (0, 105):@0.080477:0.938003:0.156444:0.938003:0.156444:0.922290:0.080477:0.922290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . :@0.156304:0.937688:0.170209:0.937688:0.170209:0.923404:0.156304:0.923404:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000