100:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000 Límites y continuidad de funciones:@0.073089:0.043661:0.383513:0.043661:0.383513:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tema 5. Límites de funciones trigonométricas, exponenciales y logarítmicas:@0.073089:0.094961:0.928971:0.094961:0.928971:0.071061:0.073089:0.071061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Calcula los siguientes límites: lim :@0.293660:0.165942:0.536393:0.165831:0.536393:0.150118:0.293660:0.150229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.506445:0.174124:0.511866:0.174124:0.511866:0.162192:0.506445:0.162192:0.000000 0:@0.522616:0.174124:0.529149:0.174124:0.529149:0.162697:0.522616:0.162697:0.000000 sen x:@0.537369:0.165831:0.578730:0.165831:0.578730:0.149425:0.537369:0.149425:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.564133:0.166413:0.585890:0.166413:0.585890:0.148759:0.564133:0.148759:0.000000:0.000000:0.000000 Reto matemático:@0.302768:0.139665:0.425244:0.139665:0.425244:0.124259:0.302768:0.124259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.00:@0.087319:0.128881:0.098283:0.128881:0.098283:0.123167:0.087319:0.123167:0.000000:0.000000:0.000000:0.000000 0.75:@0.087319:0.136445:0.098283:0.136445:0.098283:0.130732:0.087319:0.130732:0.000000:0.000000:0.000000:0.000000 0.50:@0.087319:0.145271:0.098283:0.145271:0.098283:0.139557:0.087319:0.139557:0.000000:0.000000:0.000000:0.000000 0.25:@0.087319:0.154096:0.098283:0.154096:0.098283:0.148382:0.087319:0.148382:0.000000:0.000000:0.000000:0.000000 0.00:@0.087319:0.162291:0.098283:0.162291:0.098283:0.156577:0.087319:0.156577:0.000000:0.000000:0.000000:0.000000 -0.25:@0.085325:0.170486:0.098283:0.170486:0.098283:0.164772:0.085325:0.164772:0.000000:0.000000:0.000000:0.000000:0.000000 -0.50:@0.085325:0.178680:0.098283:0.178680:0.098283:0.172967:0.085325:0.172967:0.000000:0.000000:0.000000:0.000000:0.000000 -0.75:@0.085325:0.186875:0.098283:0.186875:0.098283:0.181161:0.085325:0.181161:0.000000:0.000000:0.000000:0.000000:0.000000 -1.00:@0.085325:0.195070:0.098283:0.195070:0.098283:0.189356:0.085325:0.189356:0.000000:0.000000:0.000000:0.000000:0.000000 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0:@0.103742:0.202010:0.245498:0.202010:0.245498:0.196297:0.103742:0.196297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sin( ):@0.115090:0.129579:0.128831:0.129579:0.128831:0.123866:0.115090:0.123866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.124346:0.129579:0.127057:0.129579:0.127057:0.123614:0.124346:0.123614:0.000000 5.1 Teorema 1. Límites de funciones trigonométricas:@0.293660:0.235919:0.702807:0.235919:0.702807:0.218972:0.293660:0.218972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para todo número real en el dominio de :@0.300354:0.298064:0.613590:0.298064:0.613590:0.282351:0.300354:0.282351:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.469848:0.298064:0.477303:0.298064:0.477303:0.281658:0.469848:0.281658:0.000000 cada función::@0.300372:0.314706:0.397838:0.314706:0.397838:0.298993:0.300372:0.298993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x a:@0.300354:0.353824:0.323259:0.353824:0.323259:0.341893:0.300354:0.341893:0.000000:0.000000:0.000000 lim :@0.300354:0.345237:0.330302:0.345237:0.330302:0.329525:0.300354:0.329525:0.000000:0.000000:0.000000:0.000000 senx sena:@0.331296:0.345237:0.414607:0.345640:0.414607:0.329233:0.331296:0.328831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.366675:0.346222:0.382008:0.346222:0.382008:0.328568:0.366675:0.328568:0.000000 :@0.414569:0.345643:0.424868:0.345643:0.424868:0.329931:0.414569:0.329931:0.000000:0.000000 x a:@0.481079:0.353824:0.503985:0.353824:0.503985:0.341893:0.481079:0.341893:0.000000:0.000000:0.000000 lim :@0.481079:0.345237:0.511028:0.345237:0.511028:0.329525:0.481079:0.329525:0.000000:0.000000:0.000000:0.000000 cosx cosa:@0.512022:0.345237:0.594752:0.345640:0.594752:0.329233:0.512022:0.328831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.547401:0.346222:0.562734:0.346222:0.562734:0.328568:0.547401:0.328568:0.000000 x a:@0.300354:0.384760:0.323259:0.384760:0.323259:0.372829:0.300354:0.372829:0.000000:0.000000:0.000000 lim :@0.300354:0.376175:0.330302:0.376175:0.330302:0.360462:0.300354:0.360462:0.000000:0.000000:0.000000:0.000000 tanx tana:@0.331296:0.376175:0.415086:0.376577:0.415086:0.360171:0.331296:0.359769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.366675:0.377159:0.382008:0.377159:0.382008:0.359505:0.366675:0.359505:0.000000 :@0.415048:0.376579:0.424868:0.376579:0.424868:0.360867:0.415048:0.360867:0.000000:0.000000 x a:@0.481079:0.384760:0.503985:0.384760:0.503985:0.372829:0.481079:0.372829:0.000000:0.000000:0.000000 lim :@0.481079:0.376175:0.511028:0.376175:0.511028:0.360462:0.481079:0.360462:0.000000:0.000000:0.000000:0.000000 cotx cota:@0.512022:0.376175:0.593758:0.376577:0.593758:0.360171:0.512022:0.359769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.547401:0.377159:0.562734:0.377159:0.562734:0.359505:0.547401:0.359505:0.000000 x a:@0.300354:0.415698:0.323259:0.415698:0.323259:0.403766:0.300354:0.403766:0.000000:0.000000:0.000000 lim :@0.300354:0.407112:0.330302:0.407112:0.330302:0.391400:0.300354:0.391400:0.000000:0.000000:0.000000:0.000000 secx seca:@0.331296:0.407112:0.412480:0.407514:0.412480:0.391108:0.331296:0.390706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.366675:0.408097:0.382008:0.408097:0.382008:0.390443:0.366675:0.390443:0.000000 :@0.412434:0.407517:0.424868:0.407517:0.424868:0.391804:0.412434:0.391804:0.000000:0.000000:0.000000 x a:@0.481079:0.415698:0.503985:0.415698:0.503985:0.403766:0.481079:0.403766:0.000000:0.000000:0.000000 lim :@0.481079:0.407112:0.511028:0.407112:0.511028:0.391400:0.481079:0.391400:0.000000:0.000000:0.000000:0.000000 cscx csca:@0.512022:0.407112:0.593077:0.407514:0.593077:0.391108:0.512022:0.390706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.547401:0.408097:0.562734:0.408097:0.562734:0.390443:0.547401:0.390443:0.000000 (1, 0):@0.857355:0.339878:0.876463:0.339878:0.876463:0.331289:0.857355:0.331289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.847019:0.312481:0.853377:0.312481:0.853377:0.301658:0.847019:0.301658:0.000000 0:@0.761842:0.350563:0.766752:0.350563:0.766752:0.341974:0.761842:0.341974:0.000000 −1:@0.681446:0.350563:0.692353:0.350563:0.692353:0.341974:0.681446:0.341974:0.000000:0.000000 −1:@0.757717:0.405069:0.768624:0.405069:0.768624:0.396480:0.757717:0.396480:0.000000:0.000000 −0.5:@0.719925:0.350563:0.736420:0.350563:0.736420:0.341974:0.719925:0.341974:0.000000:0.000000:0.000000:0.000000 −0.5:@0.750921:0.375497:0.767416:0.375497:0.767416:0.366907:0.750921:0.366907:0.000000:0.000000:0.000000:0.000000 0.5:@0.806782:0.350563:0.817646:0.350563:0.817646:0.341974:0.806782:0.341974:0.000000:0.000000:0.000000 0.5:@0.756212:0.315941:0.767076:0.315941:0.767076:0.307352:0.756212:0.307352:0.000000:0.000000:0.000000 1:@0.851873:0.350563:0.856483:0.350563:0.856483:0.341974:0.851873:0.341974:0.000000 1:@0.762163:0.286596:0.766773:0.286596:0.766773:0.278007:0.762163:0.278007:0.000000 Figura 5.1:@0.734603:0.451541:0.808556:0.451541:0.808556:0.434871:0.734603:0.434871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En el punto :@0.293657:0.486045:0.380826:0.486045:0.380826:0.470332:0.293657:0.470332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P cost, sent:@0.380429:0.486045:0.458391:0.486045:0.458391:0.469639:0.380429:0.469639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.389117:0.486627:0.395246:0.486627:0.395246:0.468973:0.389117:0.468973:0.000000 )= (:@0.458383:0.486627:0.494480:0.486627:0.494480:0.468973:0.458383:0.468973:0.000000:0.000000:0.000000:0.000000 P x, y:@0.479662:0.486045:0.515519:0.486045:0.515519:0.469639:0.479662:0.469639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.515483:0.486627:0.521612:0.486627:0.521612:0.468973:0.515483:0.468973:0.000000 . Cuando se acerca al punto 1,0 , significa que el arco :@0.521520:0.486045:0.931030:0.486045:0.931030:0.470332:0.521520:0.470332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.589682:0.486045:0.598444:0.486045:0.598444:0.469639:0.589682:0.469639:0.000000 P:@0.736094:0.486045:0.744855:0.486045:0.744855:0.469639:0.736094:0.469639:0.000000 (:@0.744782:0.486627:0.750911:0.486627:0.750911:0.468973:0.744782:0.468973:0.000000 ):@0.771748:0.486627:0.777878:0.486627:0.777878:0.468973:0.771748:0.468973:0.000000 o el ángulo determinado por se acerca a cero. :@0.293638:0.502687:0.641237:0.502687:0.641237:0.486974:0.293638:0.486974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.507199:0.502687:0.515961:0.502687:0.515961:0.486281:0.507199:0.486281:0.000000 Es decir, que cuando :@0.293620:0.533627:0.447203:0.533627:0.447203:0.517914:0.293620:0.517914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t:@0.446989:0.533627:0.452364:0.533627:0.452364:0.517221:0.446989:0.517221:0.000000 0, entonces :@0.481217:0.533630:0.569778:0.533630:0.569778:0.517918:0.481217:0.517918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cost:@0.569627:0.533630:0.597852:0.533630:0.597852:0.517224:0.569627:0.517224:0.000000:0.000000:0.000000:0.000000 1 y :@0.625583:0.533630:0.650506:0.533630:0.650506:0.517918:0.625583:0.517918:0.000000:0.000000:0.000000:0.000000 sent:@0.650396:0.533630:0.679203:0.533630:0.679203:0.517224:0.650396:0.517224:0.000000:0.000000:0.000000:0.000000 0. Lo que equivale a que :@0.706941:0.533630:0.887088:0.533630:0.887088:0.517918:0.706941:0.517918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.293660:0.572749:0.299082:0.572749:0.299082:0.560817:0.293660:0.560817:0.000000 0:@0.309832:0.572749:0.316365:0.572749:0.316365:0.561322:0.309832:0.561322:0.000000 lim :@0.293660:0.564162:0.323609:0.564162:0.323609:0.548449:0.293660:0.548449:0.000000:0.000000:0.000000:0.000000 sent:@0.324603:0.564162:0.356723:0.564162:0.356723:0.547756:0.324603:0.547756:0.000000:0.000000:0.000000:0.000000 =:@0.359981:0.565147:0.375315:0.565147:0.375315:0.547492:0.359981:0.547492:0.000000 sen:@0.375223:0.564564:0.398729:0.564564:0.398729:0.548158:0.375223:0.548158:0.000000:0.000000:0.000000 0 0 :@0.398674:0.564564:0.439081:0.564568:0.439081:0.548855:0.398674:0.548851:0.000000:0.000000:0.000000:0.000000 =:@0.408687:0.565147:0.424020:0.565147:0.424020:0.547492:0.408687:0.547492:0.000000 :@0.474393:0.564568:0.478424:0.564568:0.478424:0.548855:0.474393:0.548855:0.000000 y :@0.534633:0.564568:0.552856:0.564568:0.552856:0.548855:0.534633:0.548855:0.000000:0.000000:0.000000 :@0.594889:0.564568:0.598920:0.564568:0.598920:0.548855:0.594889:0.548855:0.000000 x:@0.655112:0.572749:0.660533:0.572749:0.660533:0.560817:0.655112:0.560817:0.000000 0:@0.671283:0.572749:0.677816:0.572749:0.677816:0.561322:0.671283:0.561322:0.000000 lim :@0.655112:0.564162:0.685060:0.564162:0.685060:0.548449:0.655112:0.548449:0.000000:0.000000:0.000000:0.000000 cost:@0.686054:0.564162:0.717593:0.564162:0.717593:0.547756:0.686054:0.547756:0.000000:0.000000:0.000000:0.000000 =:@0.721433:0.565147:0.736766:0.565147:0.736766:0.547492:0.721433:0.547492:0.000000 cos:@0.736674:0.564564:0.759599:0.564564:0.759599:0.548158:0.736674:0.548158:0.000000:0.000000:0.000000 0 1. :@0.759536:0.564564:0.803135:0.564564:0.803135:0.548851:0.759536:0.548851:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.769550:0.565147:0.784883:0.565147:0.784883:0.547492:0.769550:0.547492:0.000000 Para el desarrollo del tema de límite de funciones debemos tener muy en cuenta los :@0.293648:0.595504:0.930620:0.595504:0.930620:0.579791:0.293648:0.579791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 comportamientos de las gráficas de las funciones especiales como las trigonométricas, :@0.293648:0.612146:0.931254:0.612146:0.931254:0.596433:0.293648:0.596433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las exponenciales y las logarítmicas. Así que hagamos un compendio de estas gráficas.:@0.293648:0.628788:0.918280:0.628788:0.918280:0.613075:0.293648:0.613075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.586986:0.778578:0.594087:0.778578:0.594087:0.766157:0.586986:0.766157:0.000000 0.5:@0.576495:0.735681:0.593229:0.735681:0.593229:0.723260:0.576495:0.723260:0.000000:0.000000:0.000000 1:@0.586128:0.698759:0.593229:0.698759:0.593229:0.686338:0.586128:0.686338:0.000000 1.5:@0.576489:0.661223:0.593223:0.661223:0.593223:0.648802:0.576489:0.648802:0.000000:0.000000:0.000000 −0.5:@0.570396:0.808091:0.594249:0.808091:0.594249:0.795670:0.570396:0.795670:0.000000:0.000000:0.000000:0.000000 −1:@0.579440:0.844706:0.594249:0.844706:0.594249:0.832285:0.579440:0.832285:0.000000:0.000000 1 2 3 4 5 6 7 8:@0.632003:0.778578:0.900746:0.778578:0.900746:0.766157:0.632003:0.766157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 −7 −6 −5 −4 −3 −2 −1:@0.328697:0.778578:0.563997:0.778578:0.563997:0.766157:0.328697:0.766157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.522099:0.666824:0.525184:0.666824:0.525184:0.653647:0.522099:0.653647:0.000000 p(x)= cos(x):@0.327514:0.687678:0.394972:0.687678:0.394972:0.675258:0.327514:0.675258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h(x)= sin(x):@0.347653:0.839742:0.411487:0.839742:0.411487:0.827321:0.347653:0.827321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 5.2:@0.573325:0.875214:0.647278:0.875214:0.647278:0.858545:0.573325:0.858545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En el caso de las funciones senoidales, el período es 2 y el rango es el intervalo 1,1 .:@0.293663:0.909718:0.921185:0.909718:0.921185:0.894006:0.293663:0.894006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 π:@0.680142:0.910301:0.692420:0.910301:0.692420:0.892647:0.680142:0.892647:0.000000 [–:@0.875867:0.910301:0.891108:0.910301:0.891108:0.892647:0.875867:0.892647:0.000000:0.000000 ]:@0.911945:0.910301:0.918074:0.910301:0.918074:0.892647:0.911945:0.892647:0.000000 Límites de funciones :@0.080269:0.799750:0.215916:0.799750:0.215916:0.785884:0.080269:0.785884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 trigonométricas:@0.080269:0.816392:0.183900:0.816392:0.183900:0.802526:0.080269:0.802526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t.ly/2YGgm:@0.100159:0.930570:0.180972:0.930570:0.180972:0.914857:0.100159:0.914857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 EBC 11 1. Desarrolla las propiedades del límite de una función y calcula el límite de una variedad de ellas.:@0.368133:0.970317:0.917713:0.970317:0.917713:0.958889:0.368133:0.958889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lim:@0.297929:0.188817:0.320553:0.188817:0.320553:0.174532:0.297929:0.174532:0.000000:0.000000:0.000000 x:@0.321473:0.188817:0.328251:0.188817:0.328251:0.173902:0.321473:0.173902:0.000000 0 sin:@0.355962:0.188817:0.390250:0.188817:0.390250:0.174532:0.355962:0.174532:0.000000:0.000000:0.000000:0.000000:0.000000 ( )=:@0.391153:0.189346:0.422780:0.189346:0.422780:0.173297:0.391153:0.173297:0.000000:0.000000:0.000000:0.000000 x:@0.396642:0.188817:0.403419:0.188817:0.403419:0.173902:0.396642:0.173902:0.000000 0:@0.422697:0.188817:0.430863:0.188817:0.430863:0.174532:0.422697:0.174532:0.000000 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