102:@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 0:@0.507651:0.389257:0.513922:0.389257:0.513922:0.378289:0.507651:0.378289:0.000000 11:@0.500892:0.146167:0.513434:0.146167:0.513434:0.135199:0.500892:0.135199:0.000000:0.000000 10:@0.500892:0.166913:0.513434:0.166913:0.513434:0.155945:0.500892:0.155945:0.000000:0.000000 9:@0.507163:0.187660:0.513434:0.187660:0.513434:0.176691:0.507163:0.176691:0.000000 8:@0.507163:0.208406:0.513434:0.208406:0.513434:0.197438:0.507163:0.197438:0.000000 7:@0.507163:0.229153:0.513434:0.229153:0.513434:0.218184:0.507163:0.218184:0.000000 6:@0.507163:0.249899:0.513434:0.249899:0.513434:0.238930:0.507163:0.238930:0.000000 5:@0.507163:0.272030:0.513434:0.272030:0.513434:0.261061:0.507163:0.261061:0.000000 4:@0.507163:0.294161:0.513434:0.294161:0.513434:0.283192:0.507163:0.283192:0.000000 3:@0.507163:0.317676:0.513434:0.317676:0.513434:0.306707:0.507163:0.306707:0.000000 2:@0.507163:0.341191:0.513434:0.341191:0.513434:0.330222:0.507163:0.330222:0.000000 1:@0.507163:0.361937:0.513434:0.361937:0.513434:0.350969:0.507163:0.350969:0.000000 −1:@0.500357:0.404525:0.513434:0.404525:0.513434:0.393556:0.500357:0.393556:0.000000:0.000000 1 2 3 4 5 6 7 8 9:@0.542616:0.389258:0.780541:0.389258:0.780541:0.378289:0.542616:0.378289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1:@0.214803:0.389258:0.494131:0.389258:0.494131:0.378289:0.214803:0.378289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.450351:0.290569:0.453075:0.290569:0.453075:0.278932:0.450351:0.278932:0.000000 g x = —:@0.428247:0.163145:0.483659:0.163145:0.483659:0.149325:0.428247:0.149325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.436046:0.163145:0.450544:0.163145:0.450544:0.149909:0.436046:0.149909:0.000000:0.000000:0.000000 ( ):@0.459784:0.169743:0.492031:0.169743:0.492031:0.142778:0.459784:0.142778:0.000000:0.000000:0.000000 1:@0.471041:0.158949:0.478607:0.158949:0.478607:0.145714:0.471041:0.145714:0.000000 2:@0.471041:0.168960:0.478607:0.168960:0.478607:0.155725:0.471041:0.155725:0.000000 x:@0.490856:0.155561:0.497136:0.155561:0.497136:0.141742:0.490856:0.141742:0.000000 f x = e:@0.224186:0.375981:0.266202:0.375981:0.266202:0.360306:0.224186:0.360306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.228671:0.375981:0.245115:0.375981:0.245115:0.360969:0.228671:0.360969:0.000000:0.000000:0.000000 x:@0.266724:0.370988:0.272400:0.370988:0.272400:0.358496:0.266724:0.358496:0.000000 Figura 5.5:@0.463040:0.442249:0.536993:0.442249:0.536993:0.425580:0.463040:0.425580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tengamos en cuenta el comportamiento de las gráficas de exponenciales con base mayor que 1, como en el caso de :@0.073083:0.475658:0.931452:0.475658:0.931452:0.459945:0.073083:0.459945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.073083:0.499608:0.091895:0.499608:0.091895:0.483202:0.073083:0.483202:0.000000:0.000000:0.000000 ( )=:@0.077997:0.500190:0.113892:0.500190:0.113892:0.482536:0.077997:0.482536:0.000000:0.000000:0.000000:0.000000 e:@0.114223:0.499608:0.122009:0.499608:0.122009:0.483202:0.114223:0.483202:0.000000 x:@0.122260:0.493554:0.126864:0.493554:0.126864:0.484394:0.122260:0.484394:0.000000 cuya base :@0.127026:0.499618:0.214258:0.499618:0.214258:0.483905:0.127026:0.483905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e:@0.216338:0.499618:0.224125:0.499618:0.224125:0.483212:0.216338:0.483212:0.000000 =:@0.224346:0.500201:0.239679:0.500201:0.239679:0.482546:0.224346:0.482546:0.000000 2,7182818… y con base menor que 1 y por supuesto mayor que 0, como en el caso de :@0.239992:0.499618:0.930926:0.499618:0.930926:0.483905:0.239992:0.483905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.073075:0.523568:0.091188:0.523568:0.091188:0.507162:0.073075:0.507162:0.000000:0.000000:0.000000 ( )=:@0.077695:0.524151:0.112485:0.524151:0.112485:0.506497:0.077695:0.506497:0.000000:0.000000:0.000000:0.000000 ∙ ∙:@0.112421:0.526732:0.144660:0.526732:0.144660:0.497843:0.112421:0.497843:0.000000:0.000000:0.000000 1:@0.123953:0.515533:0.132936:0.515533:0.132936:0.499820:0.123953:0.499820:0.000000 2:@0.123953:0.529512:0.132936:0.529512:0.132936:0.513799:0.123953:0.513799:0.000000 x:@0.144509:0.508447:0.149532:0.508447:0.149532:0.498454:0.144509:0.498454:0.000000 cuya base es ½ 0,5.:@0.149479:0.523572:0.301487:0.523572:0.301487:0.507860:0.149479:0.507860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.262095:0.524155:0.277428:0.524155:0.277428:0.506501:0.262095:0.506501:0.000000 0:@0.309181:0.711787:0.315549:0.711787:0.315549:0.700648:0.309181:0.700648:0.000000 8:@0.308685:0.579813:0.315053:0.579813:0.315053:0.568675:0.308685:0.568675:0.000000 6:@0.308685:0.610713:0.315053:0.610713:0.315053:0.599574:0.308685:0.599574:0.000000 4:@0.308685:0.641612:0.315053:0.641612:0.315053:0.630473:0.308685:0.630473:0.000000 2:@0.308685:0.672512:0.315053:0.672512:0.315053:0.661373:0.308685:0.661373:0.000000 −2:@0.301774:0.735809:0.315055:0.735809:0.315055:0.724671:0.301774:0.724671:0.000000:0.000000 −4:@0.301774:0.766709:0.315055:0.766709:0.315055:0.755570:0.301774:0.755570:0.000000:0.000000 −6:@0.301774:0.797608:0.315055:0.797608:0.315055:0.786469:0.301774:0.786469:0.000000:0.000000 −8:@0.301774:0.828507:0.315055:0.828507:0.315055:0.817369:0.301774:0.817369:0.000000:0.000000 1 2 3 4 5 6 7 8:@0.365842:0.711787:0.727579:0.711787:0.727579:0.700648:0.365842:0.700648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 −1:@0.261978:0.711787:0.275258:0.711787:0.275258:0.700648:0.261978:0.700648:0.000000:0.000000 :@0.250992:0.611568:0.253759:0.611568:0.253759:0.599751:0.250992:0.599751:0.000000 f x = In x:@0.331986:0.769809:0.397076:0.769809:0.397076:0.753890:0.331986:0.753890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.336539:0.772887:0.341620:0.772887:0.341620:0.763998:0.336539:0.763998:0.000000 ( ):@0.341621:0.769809:0.358320:0.769809:0.358320:0.754563:0.341621:0.754563:0.000000:0.000000:0.000000 ( ):@0.385110:0.769809:0.401809:0.769809:0.401809:0.754563:0.385110:0.754563:0.000000:0.000000:0.000000 g x = log x:@0.329630:0.615575:0.423223:0.615575:0.423223:0.597966:0.329630:0.597966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.339566:0.618980:0.345187:0.618980:0.345187:0.609148:0.339566:0.609148:0.000000 ( ):@0.345187:0.615575:0.363659:0.615575:0.363659:0.598711:0.345187:0.598711:0.000000:0.000000:0.000000 ( ):@0.409987:0.615575:0.428459:0.615575:0.428459:0.598711:0.409987:0.598711:0.000000:0.000000:0.000000 1:@0.402198:0.614927:0.407521:0.614927:0.407521:0.605615:0.402198:0.605615:0.000000 2:@0.402198:0.621971:0.407521:0.621971:0.407521:0.612658:0.402198:0.612658:0.000000 Figura 5.6:@0.463040:0.875555:0.536993:0.875555:0.536993:0.858885:0.463040:0.858885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las funciones logarítmicas son inversas de las funciones exponenciales, como en el caso de :@0.073083:0.902917:0.743037:0.902917:0.743037:0.887204:0.073083:0.887204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lnx:@0.743051:0.902917:0.763677:0.902917:0.763677:0.886511:0.743051:0.886511:0.000000:0.000000:0.000000 , que es inversa de y :@0.763612:0.902917:0.930948:0.902918:0.930948:0.887205:0.763612:0.887204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e:@0.902164:0.902917:0.909950:0.902917:0.909950:0.886511:0.902164:0.886511:0.000000 x:@0.909896:0.896854:0.914500:0.896854:0.914500:0.887693:0.909896:0.887693:0.000000 donde las imágenes de valores de cercanos a cero por la derecha tienden a :@0.073096:0.926868:0.620822:0.926868:0.620822:0.911155:0.073096:0.911155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.318520:0.926868:0.325975:0.926868:0.325975:0.910462:0.318520:0.910462:0.000000 –∞:@0.620473:0.927450:0.641770:0.927450:0.641770:0.909796:0.620473:0.909796:0.000000:0.000000 y log que es inversa de :@0.641586:0.926868:0.832797:0.926872:0.832797:0.911159:0.641586:0.911155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.684371:0.927073:0.689270:0.927073:0.689270:0.918502:0.684371:0.918502:0.000000 2:@0.684371:0.938760:0.689270:0.938760:0.689270:0.930189:0.684371:0.930189:0.000000 :@0.693462:0.926423:0.695450:0.926423:0.695450:0.922259:0.693462:0.922259:0.000000:0.000000 x:@0.695142:0.926872:0.702597:0.926872:0.702597:0.910466:0.695142:0.910466:0.000000 ∙ ∙:@0.832308:0.930031:0.864323:0.930031:0.864323:0.901142:0.832308:0.901142:0.000000:0.000000:0.000000 1:@0.843694:0.918833:0.852677:0.918833:0.852677:0.903120:0.843694:0.903120:0.000000 2:@0.843694:0.932812:0.852677:0.932812:0.852677:0.917099:0.843694:0.917099:0.000000 x:@0.864027:0.911747:0.869050:0.911747:0.869050:0.901753:0.864027:0.901753:0.000000 , donde :@0.868949:0.926872:0.930898:0.926872:0.930898:0.911159:0.868949:0.911159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las imágenes de valores de cercanos a cero por la derecha tienden a .:@0.073074:0.943514:0.595638:0.943514:0.595638:0.927801:0.073074:0.927801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.271339:0.943514:0.278794:0.943514:0.278794:0.927108:0.271339:0.927108:0.000000 ∞:@0.580249:0.944096:0.592527:0.944096:0.592527:0.926442:0.580249:0.926442:0.000000 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