146:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
Competencia :@0.199644:0.302006:0.297267:0.302006:0.297267:0.286533:0.199644:0.286533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199644:0.314574:0.311603:0.314574:0.311603:0.299101:0.199644:0.299101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los conceptos de límite :@0.193072:0.339047:0.349725:0.339047:0.349725:0.323984:0.193072:0.323984:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y continuidad son la base del :@0.153336:0.354889:0.344712:0.354889:0.344712:0.339826:0.153336:0.339826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estudio del cálculo diferencial :@0.153336:0.370731:0.347212:0.370731:0.347212:0.355668:0.153336:0.355668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del que aquí se dan los primeros :@0.153336:0.386573:0.364746:0.386573:0.364746:0.371510:0.153336:0.371510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pasos. Comencemos observan-:@0.153336:0.402415:0.354777:0.402415:0.354777:0.387352:0.153336:0.387352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
do el significado más próximo :@0.153336:0.418257:0.350959:0.418257:0.350959:0.403194:0.153336:0.403194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al matemático de la palabra “lí-:@0.153336:0.434099:0.352119:0.434099:0.352119:0.419036:0.153336:0.419036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mite”. Según el Diccionario de la :@0.153336:0.449941:0.363305:0.449941:0.363305:0.434878:0.153336:0.434878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lengua española, existen varios :@0.153336:0.465783:0.353208:0.465783:0.353208:0.450720:0.153336:0.450720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
significados: “término”, “fin”, “ex-:@0.153336:0.481625:0.356712:0.481625:0.356712:0.466562:0.153336:0.466562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tremo”, “confinante”, “ aledaño”, :@0.153336:0.497467:0.357257:0.497467:0.357257:0.482404:0.153336:0.482404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
“línea que separa dos terrenos :@0.153336:0.513309:0.349690:0.513309:0.349690:0.498246:0.153336:0.498246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
contiguos”, “punto del cual no :@0.153336:0.529151:0.350726:0.529151:0.350726:0.514088:0.153336:0.514088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se puede extender una acción, :@0.153336:0.544993:0.353034:0.544993:0.353034:0.529930:0.153336:0.529930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una influencia, un estado”. :@0.153336:0.560835:0.325347:0.560835:0.325347:0.545772:0.153336:0.545772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la palabra “continuo”, :@0.153336:0.583806:0.315937:0.583806:0.315937:0.568743:0.153336:0.568743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
encontramos los siguientes :@0.153336:0.599648:0.332366:0.599648:0.332366:0.584585:0.153336:0.584585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
significados: “sin interrupción :@0.153336:0.615490:0.346209:0.615490:0.346209:0.600427:0.153336:0.600427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el tiempo o en el espacio”, :@0.153336:0.631332:0.344222:0.631332:0.344222:0.616269:0.153336:0.616269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
“que se hace o se extiende sin :@0.153336:0.647174:0.348564:0.647174:0.348564:0.632111:0.153336:0.632111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
interrupción”, “todo compues-:@0.153336:0.663016:0.350274:0.663016:0.350274:0.647953:0.153336:0.647953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
to de partes unidas entre sí”, :@0.153336:0.678858:0.338575:0.678858:0.338575:0.663795:0.153336:0.663795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
“incesante”. :@0.153336:0.694700:0.230046:0.694700:0.230046:0.679637:0.153336:0.679637:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En cuanto  a la palabra “con-:@0.153336:0.717420:0.337766:0.717420:0.337766:0.702357:0.153336:0.702357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tinuidad”, se tiene el siguiente :@0.153336:0.733011:0.347546:0.733011:0.347546:0.717948:0.153336:0.717948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
significado: “calidad o condición :@0.153336:0.748602:0.365222:0.748602:0.365222:0.733539:0.153336:0.733539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de las funciones o transforma-:@0.153336:0.764193:0.349375:0.764193:0.349375:0.749130:0.153336:0.749130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciones continuas”.:@0.153336:0.779784:0.269007:0.779784:0.269007:0.764721:0.153336:0.764721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Intuitivamente, la palabra “límite” :@0.153336:0.802372:0.364432:0.802372:0.364432:0.787309:0.153336:0.787309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en matemática debe ser asociada :@0.153336:0.817832:0.365277:0.817832:0.365277:0.802768:0.153336:0.802768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a las ideas de proximidad, ten-:@0.153336:0.833291:0.342322:0.833291:0.342322:0.818228:0.153336:0.818228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dencia, aproximación y esta, a su :@0.153336:0.848750:0.360971:0.848750:0.360971:0.833687:0.153336:0.833687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vez, debe asociarse a la idea de :@0.153336:0.864209:0.348654:0.864209:0.348654:0.849146:0.153336:0.849146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cercanía a un punto, a un valor :@0.153336:0.879668:0.350274:0.879668:0.350274:0.864605:0.153336:0.864605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
numérico, o también de tenden-:@0.153336:0.895127:0.358399:0.895127:0.358399:0.880064:0.153336:0.880064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cia a alejarse como se quiera.:@0.153336:0.910586:0.332262:0.910586:0.332262:0.895523:0.153336:0.895523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.47. Calcular de manera intuitiva la derivada de funciones polinomiales de grado ≤ 4 a partir del cociente incremental.:@0.143847:0.947781:0.672829:0.947781:0.672829:0.937739:0.143847:0.937739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Derivadas a partir del cociente :@0.404235:0.116974:0.794029:0.116974:0.794029:0.072315:0.404235:0.072315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incremental:@0.404235:0.154693:0.553699:0.154693:0.553699:0.110034:0.404235:0.110034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Asumimos, sin demostración, que las funciones polinomiales de gra-:@0.404236:0.178335:0.891757:0.178335:0.891757:0.161837:0.404236:0.161837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
do ≤ 4 son funciones continuas. Con esta premisa, las nociones que :@0.404236:0.195686:0.895939:0.195686:0.895939:0.179188:0.404236:0.179188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
introducimos en esta sección corresponden a los primeros pasos que :@0.404236:0.213036:0.895897:0.213036:0.895897:0.196539:0.404236:0.196539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se dan en el cálculo diferencial.:@0.404236:0.230387:0.621411:0.230387:0.621411:0.213890:0.404236:0.213890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.404236:0.260780:0.491103:0.260780:0.491103:0.243834:0.404236:0.243834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sea  ,      .  La distancia de   a   se denota  ( ,  ), y se :@0.484322:0.260317:0.895905:0.260317:0.895905:0.243820:0.484322:0.243820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.519905:0.260433:0.542233:0.260433:0.542233:0.243964:0.519905:0.243964:0.000000:0.000000:0.000000
:@0.547030:0.260100:0.563078:0.260100:0.563078:0.245453:0.547030:0.245453:0.000000
:@0.568261:0.259349:0.582170:0.259349:0.582170:0.245902:0.568261:0.245902:0.000000
x y:@0.703676:0.260433:0.735502:0.260433:0.735502:0.243964:0.703676:0.243964:0.000000:0.000000:0.000000
d x y:@0.814374:0.260433:0.851845:0.260433:0.851845:0.243964:0.814374:0.243964:0.000000:0.000000:0.000000:0.000000:0.000000
lee “distancia de   a  ”. Se define como  ( ,  ) = |  –  |.:@0.404236:0.277668:0.788767:0.277668:0.788767:0.261170:0.404236:0.261170:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.522234:0.277784:0.553521:0.277784:0.553521:0.261315:0.522234:0.261315:0.000000:0.000000:0.000000
d x y:@0.679822:0.277784:0.717004:0.277784:0.717004:0.261315:0.679822:0.261315:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.747058:0.277784:0.781003:0.277784:0.781003:0.261315:0.747058:0.261315:0.000000:0.000000:0.000000
 :@0.404236:0.290247:0.408378:0.290247:0.408378:0.273750:0.404236:0.273750:0.000000
De la definición de valor absoluto y de la distancia entre dos números :@0.404236:0.307598:0.895957:0.307598:0.895957:0.291100:0.404236:0.291100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales, tenemos::@0.404236:0.324949:0.516144:0.324949:0.516144:0.308451:0.404236:0.308451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d x y:@0.427971:0.349544:0.465153:0.349544:0.465153:0.333075:0.427971:0.333075:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) =   –  , si   ≥  ,:@0.437141:0.349428:0.582247:0.349428:0.582247:0.332930:0.437141:0.332930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.490198:0.349544:0.524143:0.349544:0.524143:0.333075:0.490198:0.333075:0.000000:0.000000:0.000000
x y:@0.545239:0.349544:0.579492:0.349544:0.579492:0.333075:0.545239:0.333075:0.000000:0.000000:0.000000
d( ,  ) =   –  , si   <  .:@0.427971:0.366779:0.582767:0.366779:0.582767:0.350281:0.427971:0.350281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.443614:0.366894:0.465673:0.366894:0.465673:0.350426:0.443614:0.350426:0.000000:0.000000:0.000000
y x:@0.490718:0.366894:0.524663:0.366894:0.524663:0.350426:0.490718:0.350426:0.000000:0.000000:0.000000
x y:@0.545759:0.366894:0.580012:0.366894:0.580012:0.350426:0.545759:0.350426:0.000000:0.000000:0.000000
A la distancia entre dos números reales arriba definida la denomina-:@0.404236:0.395451:0.891784:0.395451:0.891784:0.378953:0.404236:0.378953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
remos métrica usual en  , y, como se dijo, esta nos permite medir la :@0.404236:0.412801:0.895905:0.412801:0.895905:0.396304:0.404236:0.396304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.574695:0.411833:0.588605:0.411833:0.588605:0.398386:0.574695:0.398386:0.000000
proximidad o lejanía entre dos números reales. Sea 0 <  < 1,  ,      , :@0.404236:0.430152:0.895906:0.430133:0.895906:0.413636:0.404236:0.413655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
δ:@0.786705:0.437207:0.795940:0.437207:0.795940:0.419072:0.786705:0.419072:0.000000
 :@0.795939:0.429483:0.800755:0.429483:0.800755:0.415183:0.795939:0.415183:0.000000
x y:@0.829981:0.430249:0.851596:0.430249:0.851596:0.413780:0.829981:0.413780:0.000000:0.000000:0.000000
:@0.855372:0.429916:0.871420:0.429916:0.871420:0.415270:0.855372:0.415270:0.000000
:@0.875196:0.429165:0.889106:0.429165:0.889106:0.415718:0.875196:0.415718:0.000000
se dice que   es próximo a   respecto de   si y solo si se verifica::@0.404238:0.447484:0.847277:0.447484:0.847277:0.430986:0.404238:0.430986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.486443:0.447600:0.494130:0.447600:0.494130:0.431131:0.486443:0.431131:0.000000
x:@0.592170:0.447600:0.599645:0.447600:0.599645:0.431131:0.592170:0.431131:0.000000
δ:@0.689972:0.454558:0.699207:0.454558:0.699207:0.436423:0.689972:0.436423:0.000000
d x y:@0.580339:0.464951:0.617039:0.464951:0.617039:0.448482:0.580339:0.448482:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) = |  –  | <  .:@0.589413:0.464835:0.715674:0.464835:0.715674:0.448337:0.589413:0.448337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.646515:0.464951:0.680075:0.464951:0.680075:0.448482:0.646515:0.448482:0.000000:0.000000:0.000000
δ:@0.703685:0.471909:0.712920:0.471909:0.712920:0.453773:0.703685:0.453773:0.000000
En primer año de BGU se estudió, de forma intuitiva, la derivada :@0.404232:0.494765:0.895843:0.494765:0.895843:0.478267:0.404232:0.478267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de funciones cuadráticas, llamadas también funciones polinomiales :@0.404232:0.512116:0.895920:0.512116:0.895920:0.495618:0.404232:0.495618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de grado ≤ 2. En esta sección, continuamos con la metodología ahí :@0.404232:0.529466:0.895843:0.529466:0.895843:0.512969:0.404232:0.512969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
establecida para funciones polinomiales de la forma::@0.404232:0.546817:0.783083:0.546817:0.783083:0.530319:0.404232:0.530319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.491831:0.571412:0.514526:0.571412:0.514526:0.554943:0.491831:0.554943:0.000000:0.000000:0.000000
( ) =   + :@0.501098:0.571296:0.572589:0.571291:0.572589:0.554793:0.501098:0.554799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.539570:0.571412:0.548548:0.571412:0.548548:0.554943:0.539570:0.554943:0.000000
0:@0.548543:0.574567:0.553496:0.574567:0.553496:0.564949:0.548543:0.564949:0.000000
a x a x:@0.572589:0.571406:0.634490:0.571406:0.634490:0.554937:0.572589:0.554937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.581565:0.574567:0.586519:0.574567:0.586519:0.564949:0.581565:0.564949:0.000000
 + :@0.593994:0.571291:0.613086:0.571291:0.613086:0.554793:0.593994:0.554793:0.000000:0.000000:0.000000
2:@0.622063:0.574567:0.627016:0.574567:0.627016:0.564949:0.622063:0.564949:0.000000
2:@0.634490:0.564938:0.639443:0.564938:0.639443:0.555319:0.634490:0.555319:0.000000
 + :@0.639443:0.571291:0.658535:0.571291:0.658535:0.554793:0.639443:0.554793:0.000000:0.000000:0.000000
a x:@0.658535:0.571406:0.679940:0.571406:0.679940:0.554937:0.658535:0.554937:0.000000:0.000000:0.000000
3:@0.667512:0.574567:0.672465:0.574567:0.672465:0.564949:0.667512:0.564949:0.000000
3:@0.679940:0.564938:0.684894:0.564938:0.684894:0.555319:0.679940:0.555319:0.000000
 + :@0.684892:0.571291:0.703984:0.571291:0.703984:0.554793:0.684892:0.554793:0.000000:0.000000:0.000000
a x:@0.703984:0.571406:0.725390:0.571406:0.725390:0.554937:0.703984:0.554937:0.000000:0.000000:0.000000
4:@0.712961:0.574567:0.717914:0.574567:0.717914:0.564949:0.712961:0.564949:0.000000
4:@0.725390:0.564938:0.730343:0.564938:0.730343:0.555319:0.725390:0.555319:0.000000
,        ,:@0.730342:0.571291:0.804178:0.571291:0.804178:0.554793:0.730342:0.554793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.745523:0.578877:0.757095:0.578877:0.757095:0.559878:0.745523:0.559878:0.000000
x:@0.757104:0.571406:0.764579:0.571406:0.764579:0.554937:0.757104:0.554937:0.000000
:@0.768720:0.570772:0.783372:0.570772:0.783372:0.557399:0.768720:0.557399:0.000000
:@0.787513:0.570322:0.801423:0.570322:0.801423:0.556875:0.787513:0.556875:0.000000
 :@0.404231:0.583870:0.408373:0.583870:0.408373:0.567372:0.404231:0.567372:0.000000
donde  ,  ,  ,       fijos. El conjunto de todas las funciones po-:@0.404231:0.601221:0.891738:0.601214:0.891738:0.584717:0.404231:0.584723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a a a a:@0.456035:0.601336:0.529822:0.601330:0.529822:0.584861:0.456035:0.584868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.465021:0.604491:0.469974:0.604491:0.469974:0.594873:0.465021:0.594873:0.000000
1:@0.486623:0.604491:0.491576:0.604491:0.491576:0.594873:0.486623:0.594873:0.000000
2:@0.508223:0.604491:0.513177:0.604491:0.513177:0.594873:0.508223:0.594873:0.000000
3:@0.529826:0.604491:0.534779:0.604491:0.534779:0.594873:0.529826:0.594873:0.000000
:@0.539696:0.600696:0.554349:0.600696:0.554349:0.587322:0.539696:0.587322:0.000000
:@0.559260:0.600246:0.573170:0.600246:0.573170:0.586799:0.559260:0.586799:0.000000
linomiales de grado ≤ 4 con coeficientes reales se denota con  [ ]. :@0.404233:0.618565:0.895912:0.618565:0.895912:0.602067:0.404233:0.602067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.850222:0.618681:0.859007:0.618681:0.859007:0.602212:0.850222:0.602212:0.000000
4:@0.859045:0.621842:0.863999:0.621842:0.863999:0.612224:0.859045:0.612224:0.000000
:@0.869856:0.617478:0.883160:0.617478:0.883160:0.604616:0.869856:0.604616:0.000000
 :@0.891770:0.618565:0.895912:0.618565:0.895912:0.602067:0.891770:0.602067:0.000000
Se tiene la siguiente equivalencia::@0.404244:0.635916:0.638008:0.635916:0.638008:0.619418:0.404244:0.619418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.526540:0.660511:0.535806:0.660511:0.535806:0.644042:0.526540:0.644042:0.000000
    [ ]   :@0.535806:0.660395:0.624040:0.660394:0.624040:0.643897:0.535806:0.643897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.539939:0.659876:0.554591:0.659876:0.554591:0.646502:0.539939:0.646502:0.000000
P:@0.558734:0.660510:0.567519:0.660510:0.567519:0.644041:0.558734:0.644041:0.000000
4 :@0.567518:0.663672:0.574886:0.663672:0.574886:0.654054:0.567518:0.654054:0.000000:0.000000
:@0.580743:0.659307:0.594048:0.659307:0.594048:0.646445:0.580743:0.646445:0.000000
∃:@0.624039:0.667468:0.634365:0.667468:0.634365:0.649333:0.624039:0.649333:0.000000
a a a a a:@0.634364:0.660510:0.726649:0.660510:0.726649:0.644041:0.634364:0.644041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.643341:0.663672:0.648295:0.663672:0.648295:0.654054:0.643341:0.654054:0.000000
,  ,  ,  , :@0.648293:0.660394:0.717672:0.660394:0.717672:0.643897:0.648293:0.643897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.664168:0.663672:0.669121:0.663672:0.669121:0.654054:0.664168:0.654054:0.000000
2:@0.684995:0.663672:0.689948:0.663672:0.689948:0.654054:0.684995:0.654054:0.000000
3:@0.705823:0.663672:0.710776:0.663672:0.710776:0.654054:0.705823:0.654054:0.000000
4 :@0.726649:0.663672:0.734018:0.663672:0.734018:0.654054:0.726649:0.654054:0.000000:0.000000
:@0.734017:0.659876:0.748670:0.659876:0.748670:0.646502:0.734017:0.646502:0.000000
  , :@0.748670:0.660394:0.773619:0.660394:0.773619:0.643897:0.748670:0.643897:0.000000:0.000000:0.000000:0.000000
:@0.752813:0.659425:0.766722:0.659425:0.766722:0.645979:0.752813:0.645979:0.000000
tal que  ( ) =   + :@0.404246:0.689066:0.538283:0.689061:0.538283:0.672563:0.404246:0.672569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.457534:0.689182:0.480228:0.689182:0.480228:0.672713:0.457534:0.672713:0.000000:0.000000:0.000000
a:@0.505273:0.689182:0.514251:0.689182:0.514251:0.672713:0.505273:0.672713:0.000000
0:@0.514239:0.692339:0.519192:0.692339:0.519192:0.682720:0.514239:0.682720:0.000000
a x a x:@0.538283:0.689176:0.600186:0.689176:0.600186:0.672708:0.538283:0.672708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.547260:0.692339:0.552213:0.692339:0.552213:0.682720:0.547260:0.682720:0.000000
 + :@0.559688:0.689061:0.578780:0.689061:0.578780:0.672563:0.559688:0.672563:0.000000:0.000000:0.000000
2:@0.587757:0.692339:0.592710:0.692339:0.592710:0.682720:0.587757:0.682720:0.000000
2:@0.600184:0.682709:0.605137:0.682709:0.605137:0.673091:0.600184:0.673091:0.000000
 + :@0.605138:0.689061:0.624229:0.689061:0.624229:0.672563:0.605138:0.672563:0.000000:0.000000:0.000000
a x:@0.624229:0.689176:0.645635:0.689176:0.645635:0.672708:0.624229:0.672708:0.000000:0.000000:0.000000
3:@0.633206:0.692339:0.638159:0.692339:0.638159:0.682720:0.633206:0.682720:0.000000
3:@0.645635:0.682709:0.650588:0.682709:0.650588:0.673091:0.645635:0.673091:0.000000
 + :@0.650587:0.689061:0.669679:0.689061:0.669679:0.672563:0.650587:0.672563:0.000000:0.000000:0.000000
a x:@0.669679:0.689176:0.691084:0.689176:0.691084:0.672708:0.669679:0.672708:0.000000:0.000000:0.000000
4:@0.678656:0.692339:0.683609:0.692339:0.683609:0.682720:0.678656:0.682720:0.000000
4:@0.691084:0.682709:0.696037:0.682709:0.696037:0.673091:0.691084:0.673091:0.000000
,        .:@0.696038:0.689061:0.769874:0.689061:0.769874:0.672563:0.696038:0.672563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.711217:0.696647:0.722790:0.696647:0.722790:0.677648:0.711217:0.677648:0.000000
x:@0.722798:0.689176:0.730273:0.689176:0.730273:0.672708:0.722798:0.672708:0.000000
:@0.734414:0.688542:0.749067:0.688542:0.749067:0.675169:0.734414:0.675169:0.000000
:@0.753210:0.688092:0.767119:0.688092:0.767119:0.674645:0.753210:0.674645:0.000000
 :@0.404239:0.701640:0.408381:0.701640:0.408381:0.685142:0.404239:0.685142:0.000000
Recordemos que  [ ], con las operaciones habituales de adición y :@0.404239:0.718991:0.895956:0.718984:0.895956:0.702487:0.404239:0.702493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.531118:0.719106:0.539903:0.719106:0.539903:0.702638:0.531118:0.702638:0.000000
4:@0.539887:0.722262:0.544840:0.722262:0.544840:0.712644:0.539887:0.712644:0.000000
:@0.550697:0.717897:0.564002:0.717897:0.564002:0.705035:0.550697:0.705035:0.000000
producto de polinomios por números reales, es un espacio vectorial :@0.404235:0.736335:0.895916:0.736335:0.895916:0.719838:0.404235:0.719838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
real.:@0.404235:0.753686:0.432016:0.753686:0.432016:0.737188:0.404235:0.737188:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.404235:0.784079:0.491102:0.784079:0.491102:0.767133:0.404235:0.767133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean      [ ], :@0.484321:0.783616:0.612443:0.783610:0.612443:0.767112:0.484321:0.767118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.530307:0.783732:0.539574:0.783732:0.539574:0.767263:0.530307:0.767263:0.000000
:@0.544444:0.783091:0.559096:0.783091:0.559096:0.769718:0.544444:0.769718:0.000000
P:@0.563950:0.783725:0.572735:0.783725:0.572735:0.767257:0.563950:0.767257:0.000000
4 :@0.572742:0.786888:0.580110:0.786888:0.580110:0.777270:0.572742:0.777270:0.000000:0.000000
:@0.586385:0.782523:0.599690:0.782523:0.599690:0.769661:0.586385:0.769661:0.000000
a:@0.613156:0.783725:0.622134:0.783725:0.622134:0.767257:0.613156:0.767257:0.000000
 :@0.622138:0.786888:0.624553:0.786888:0.624553:0.777270:0.622138:0.777270:0.000000
:@0.624972:0.783091:0.639625:0.783091:0.639625:0.769718:0.624972:0.769718:0.000000
   fijo, :@0.639624:0.783610:0.692372:0.783610:0.692372:0.767112:0.639624:0.767112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.644479:0.782641:0.658388:0.782641:0.658388:0.769194:0.644479:0.769194:0.000000
h:@0.693085:0.783725:0.702487:0.783725:0.702487:0.767257:0.693085:0.767257:0.000000
 :@0.702504:0.786888:0.704919:0.786888:0.704919:0.777270:0.702504:0.777270:0.000000
:@0.705337:0.783091:0.719990:0.783091:0.719990:0.769718:0.705337:0.769718:0.000000
  ,  tal que   ≠ 0. El co-:@0.719990:0.783610:0.891719:0.783610:0.891719:0.767112:0.719990:0.767112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.724845:0.782641:0.738755:0.782641:0.738755:0.769194:0.724845:0.769194:0.000000
h:@0.805931:0.783725:0.815332:0.783725:0.815332:0.767257:0.805931:0.767257:0.000000
ciente incremental de la función polinomial   en el punto   se denota   :@0.404233:0.800960:0.895884:0.800960:0.895884:0.784463:0.404233:0.784463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.713997:0.801076:0.723264:0.801076:0.723264:0.784607:0.713997:0.784607:0.000000
a:@0.810343:0.801076:0.819320:0.801076:0.819320:0.784607:0.810343:0.784607:0.000000
Q h:@0.404233:0.818427:0.431474:0.818427:0.431474:0.801958:0.404233:0.801958:0.000000:0.000000:0.000000
( ) y se define como sigue::@0.416119:0.818311:0.605609:0.818311:0.605609:0.801814:0.416119:0.801814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.560416:0.842906:0.587657:0.842906:0.587657:0.826437:0.560416:0.826437:0.000000:0.000000:0.000000
( ) =                              .:@0.572303:0.842790:0.735576:0.842790:0.735576:0.826293:0.572303:0.826293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En general, los valores de | | ≠ 0 son suficientemente pequeños; esto :@0.404233:0.875222:0.895936:0.875222:0.895936:0.858724:0.404233:0.858724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.588983:0.875337:0.598384:0.875337:0.598384:0.858869:0.588983:0.858869:0.000000
es, si 0 <   < 1, 0 < | | <  . Este cociente incremental tiene muchas :@0.404233:0.892572:0.895903:0.892579:0.895903:0.876081:0.404233:0.876075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
δ:@0.470840:0.899653:0.480075:0.899653:0.480075:0.881517:0.470840:0.881517:0.000000
h:@0.551096:0.892694:0.560498:0.892694:0.560498:0.876226:0.551096:0.876226:0.000000
δ:@0.586204:0.899653:0.595439:0.899653:0.595439:0.881517:0.586204:0.881517:0.000000
aplicaciones, y es un paso previo al cálculo de la derivada de una :@0.404240:0.909929:0.895857:0.909929:0.895857:0.893432:0.404240:0.893432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función.:@0.404240:0.927280:0.462499:0.927280:0.462499:0.910783:0.404240:0.910783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.097890:0.307805:0.097890:0.307805:0.082418:0.199646:0.082418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo explicas qué es :@0.199884:0.126518:0.350081:0.126518:0.350081:0.111455:0.199884:0.111455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una función continua? :@0.153341:0.142360:0.302836:0.142360:0.302836:0.127297:0.153341:0.127297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.193038:0.363493:0.193038:0.363493:0.177565:0.199646:0.177565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué aplicaciones tiene :@0.199884:0.221665:0.356627:0.221665:0.356627:0.206602:0.199884:0.206602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el cálculo del cociente  :@0.153341:0.237507:0.304083:0.237507:0.304083:0.222444:0.153341:0.222444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incremental?:@0.153341:0.253349:0.236241:0.253349:0.236241:0.238286:0.153341:0.238286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p a + h:@0.617668:0.836731:0.670436:0.836731:0.670436:0.820262:0.617668:0.820262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.626935:0.836615:0.632888:0.836615:0.632888:0.820117:0.626935:0.820117:0.000000
) –  ( ):@0.670436:0.836615:0.725323:0.836615:0.725323:0.820117:0.670436:0.820117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p a:@0.695173:0.836731:0.719370:0.836731:0.719370:0.820262:0.695173:0.820262:0.000000:0.000000:0.000000
h:@0.666795:0.853069:0.676196:0.853069:0.676196:0.836601:0.666795:0.836601:0.000000