194:@0.026565:0.967627:0.050760:0.967627:0.050760:0.951847:0.026565:0.951847:0.000000:0.000000:0.000000
Noción de derivada. Cociente incremental:@0.404235:0.117192:0.881075:0.117192:0.881075:0.072532:0.404235:0.072532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.33. Calcular de manera intuitiva la derivada de funciones cuadráticas, a partir del cociente incremental.:@0.143847:0.952364:0.610351:0.952364:0.610351:0.942321:0.143847:0.942321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el cálculo de la derivada de una función, aparece el denominado :@0.404236:0.165812:0.895837:0.165812:0.895837:0.149315:0.404236:0.149315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cociente incremental, al que definimos a continuación.:@0.404236:0.183163:0.792389:0.183163:0.792389:0.166665:0.404236:0.166665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición. :@0.404236:0.221089:0.492450:0.221089:0.492450:0.204143:0.404236:0.204143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.493434:0.220626:0.531233:0.220626:0.531233:0.204128:0.493434:0.204128:0.000000:0.000000:0.000000:0.000000:0.000000
A, B :@0.532254:0.220742:0.565255:0.220742:0.565255:0.204273:0.532254:0.204273:0.000000:0.000000:0.000000:0.000000:0.000000
dos intervalos de  ,   una función de   en  , :@0.566276:0.220626:0.895943:0.220626:0.895943:0.204128:0.566276:0.204128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.694178:0.219657:0.708088:0.219657:0.708088:0.206211:0.694178:0.206211:0.000000
f:@0.715967:0.220742:0.720263:0.220742:0.720263:0.204273:0.715967:0.204273:0.000000
A:@0.840710:0.220742:0.851980:0.220742:0.851980:0.204273:0.840710:0.204273:0.000000
B:@0.879857:0.220742:0.889046:0.220742:0.889046:0.204273:0.879857:0.204273:0.000000
 :@0.891763:0.220626:0.895905:0.220626:0.895905:0.204128:0.891763:0.204128:0.000000
a   A:@0.404236:0.240854:0.445965:0.240854:0.445965:0.224385:0.404236:0.224385:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.417086:0.241288:0.430822:0.241288:0.430822:0.222448:0.417086:0.222448:0.000000
 fijo y   :@0.445965:0.240739:0.501372:0.240739:0.501372:0.224241:0.445965:0.224241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.487828:0.240854:0.497230:0.240854:0.497230:0.224385:0.487828:0.224385:0.000000
∈ :@0.501083:0.241288:0.519635:0.241288:0.519635:0.222448:0.501083:0.222448:0.000000:0.000000
R:@0.519327:0.239770:0.533236:0.239770:0.533236:0.226323:0.519327:0.226323:0.000000
, tal que :@0.533236:0.240739:0.592882:0.240739:0.592882:0.224241:0.533236:0.224241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h ≠ :@0.592612:0.240854:0.620913:0.240854:0.620913:0.224385:0.592612:0.224385:0.000000:0.000000:0.000000:0.000000
0, y,  + :@0.620643:0.240739:0.677225:0.240739:0.677225:0.224241:0.620643:0.224241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a  h   A.:@0.649444:0.240854:0.722344:0.240854:0.722344:0.224385:0.649444:0.224385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.690229:0.241288:0.703965:0.241288:0.703965:0.222448:0.690229:0.222448:0.000000
 El cociente incremental :@0.722344:0.240739:0.895943:0.240739:0.895943:0.224241:0.722344:0.224241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la función  en el punto  se denota :@0.404255:0.260851:0.682598:0.260851:0.682598:0.244353:0.404255:0.244353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.501177:0.260967:0.509615:0.260967:0.509615:0.244498:0.501177:0.244498:0.000000:0.000000
a :@0.595557:0.260967:0.608677:0.260967:0.608677:0.244498:0.595557:0.244498:0.000000:0.000000
Q(h) :@0.682598:0.260967:0.718894:0.260967:0.718894:0.244498:0.682598:0.244498:0.000000:0.000000:0.000000:0.000000:0.000000
y se define como sigue::@0.718894:0.260851:0.882935:0.260851:0.882935:0.244353:0.718894:0.244353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.531161:0.292441:0.561446:0.292441:0.561446:0.275973:0.531161:0.275973:0.000000:0.000000:0.000000
( ):@0.544930:0.295996:0.567990:0.295996:0.567990:0.274505:0.544930:0.274505:0.000000:0.000000:0.000000
=:@0.570686:0.292962:0.581263:0.292962:0.581263:0.276681:0.570686:0.276681:0.000000
f a h:@0.588911:0.282219:0.636535:0.282219:0.636535:0.265750:0.588911:0.265750:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.614418:0.282739:0.624995:0.282739:0.624995:0.266459:0.614418:0.266459:0.000000
(:@0.597019:0.285780:0.603435:0.285780:0.603435:0.264290:0.597019:0.264290:0.000000
):@0.636648:0.285780:0.643063:0.285780:0.643063:0.264290:0.636648:0.264290:0.000000
–:@0.644920:0.282110:0.655419:0.282110:0.655419:0.265612:0.644920:0.265612:0.000000
f a:@0.660775:0.282226:0.684991:0.282226:0.684991:0.265757:0.660775:0.265757:0.000000:0.000000:0.000000
( ):@0.668897:0.285780:0.691534:0.285780:0.691534:0.264290:0.668897:0.264290:0.000000:0.000000:0.000000
h:@0.634030:0.303797:0.643432:0.303797:0.643432:0.287328:0.634030:0.287328:0.000000
Q h:@0.531161:0.341280:0.561446:0.341280:0.561446:0.324811:0.531161:0.324811:0.000000:0.000000:0.000000
( ):@0.544930:0.344835:0.567990:0.344835:0.567990:0.323344:0.544930:0.323344:0.000000:0.000000:0.000000
=:@0.570686:0.341800:0.581263:0.341800:0.581263:0.325520:0.570686:0.325520:0.000000
f:@0.588911:0.331057:0.593207:0.331057:0.593207:0.314589:0.588911:0.314589:0.000000
–2:@0.603726:0.330942:0.622645:0.330942:0.622645:0.314444:0.603726:0.314444:0.000000:0.000000
+:@0.624417:0.331578:0.634994:0.331578:0.634994:0.315297:0.624417:0.315297:0.000000
h:@0.637132:0.331057:0.646534:0.331057:0.646534:0.314589:0.637132:0.314589:0.000000
(:@0.597019:0.334619:0.603435:0.334619:0.603435:0.313128:0.597019:0.313128:0.000000
):@0.646647:0.334619:0.653062:0.334619:0.653062:0.313128:0.646647:0.313128:0.000000
–:@0.654919:0.330949:0.665419:0.330949:0.665419:0.314451:0.654919:0.314451:0.000000
f:@0.670774:0.331064:0.675071:0.331064:0.675071:0.314596:0.670774:0.314596:0.000000
–2:@0.685589:0.330949:0.704508:0.330949:0.704508:0.314451:0.685589:0.314451:0.000000:0.000000
( ):@0.678897:0.334619:0.711532:0.334619:0.711532:0.313128:0.678897:0.313128:0.000000:0.000000:0.000000
h:@0.644030:0.352635:0.653431:0.352635:0.653431:0.336166:0.644030:0.336166:0.000000
=:@0.715755:0.341805:0.726331:0.341805:0.726331:0.325524:0.715755:0.325524:0.000000
–5 2 – –5:@0.730415:0.330946:0.821174:0.330946:0.821174:0.314448:0.730415:0.314448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.750682:0.331582:0.761259:0.331582:0.761259:0.315302:0.750682:0.315302:0.000000
h:@0.772163:0.331062:0.781565:0.331062:0.781565:0.314593:0.772163:0.314593:0.000000
( ):@0.795535:0.334619:0.827766:0.334619:0.827766:0.313128:0.795535:0.313128:0.000000:0.000000:0.000000
h:@0.774647:0.352635:0.784048:0.352635:0.784048:0.336166:0.774647:0.336166:0.000000
=:@0.831980:0.341805:0.842557:0.341805:0.842557:0.325524:0.831980:0.325524:0.000000
2:@0.845119:0.341169:0.853615:0.341169:0.853615:0.324671:0.845119:0.324671:0.000000
,   h ≠ :@0.698554:0.291281:0.742402:0.291281:0.742402:0.274812:0.698554:0.274812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0.:@0.742402:0.291165:0.753653:0.291165:0.753653:0.274667:0.742402:0.274667:0.000000:0.000000
En general, los valores de |  ≠ 0 son suficientemente pequeños. :@0.404239:0.321211:0.860124:0.321211:0.860124:0.304713:0.404239:0.304713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h|:@0.588411:0.321327:0.602648:0.321327:0.602648:0.304858:0.588411:0.304858:0.000000:0.000000
Ejercicios resueltos:@0.404239:0.356288:0.534894:0.356288:0.534894:0.339501:0.404239:0.339501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404239:0.373480:0.416511:0.373480:0.416511:0.356765:0.404239:0.356765:0.000000:0.000000
 :@0.416511:0.373726:0.420537:0.373726:0.420537:0.356780:0.416511:0.356780:0.000000
Sea  la función real definida como :@0.427973:0.373263:0.696163:0.373263:0.696163:0.356765:0.427973:0.356765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.459453:0.373379:0.467891:0.373379:0.467891:0.356910:0.459453:0.356910:0.000000:0.000000
f(x) = 2x :@0.699381:0.373379:0.767310:0.373379:0.767310:0.356910:0.699381:0.356910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
– 1 con x    .  :@0.770527:0.373263:0.895888:0.373263:0.895888:0.356765:0.770527:0.356765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.796882:0.373379:0.801024:0.373379:0.801024:0.356910:0.796882:0.356910:0.000000
∈:@0.853967:0.373813:0.867703:0.373813:0.867703:0.354973:0.853967:0.354973:0.000000
R:@0.875082:0.372294:0.888991:0.372294:0.888991:0.358848:0.875082:0.358848:0.000000
 :@0.891746:0.373263:0.895888:0.373263:0.895888:0.356765:0.891746:0.356765:0.000000
Fijemos el punto  = –2. Sea  = –2 +    con  :@0.427954:0.390614:0.777753:0.390614:0.777753:0.374116:0.427954:0.374116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.556511:0.390730:0.569631:0.390730:0.569631:0.374261:0.556511:0.374261:0.000000:0.000000
x :@0.646538:0.390730:0.658155:0.390730:0.658155:0.374261:0.646538:0.374261:0.000000:0.000000
h:@0.718994:0.390730:0.728396:0.390730:0.728396:0.374261:0.718994:0.374261:0.000000
h ≠ :@0.779699:0.390730:0.810215:0.390730:0.810215:0.374261:0.779699:0.374261:0.000000:0.000000:0.000000:0.000000
0, tenemos  :@0.812161:0.390614:0.895907:0.390614:0.895907:0.374116:0.812161:0.374116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.427973:0.408080:0.432270:0.408080:0.432270:0.391612:0.427973:0.391612:0.000000
(–2) = 2(–2) –1 = –5, y,   (–2 +  ) = –5 + 2 Note que si | | es :@0.432270:0.407965:0.895907:0.407965:0.895907:0.391467:0.432270:0.391467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.614039:0.408080:0.618335:0.408080:0.618335:0.391612:0.614039:0.391612:0.000000
h:@0.663917:0.408080:0.673319:0.408080:0.673319:0.391612:0.663917:0.391612:0.000000
h. :@0.748029:0.408080:0.764116:0.408080:0.764116:0.391612:0.748029:0.391612:0.000000:0.000000:0.000000
h:@0.858070:0.408080:0.867472:0.408080:0.867472:0.391612:0.858070:0.391612:0.000000
suficientemente pequeño, 2| | también lo es. El cociente incre-:@0.427973:0.425315:0.891765:0.425315:0.891765:0.408818:0.427973:0.408818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.635114:0.425431:0.644515:0.425431:0.644515:0.408962:0.635114:0.408962:0.000000
mental está definido como: :@0.427973:0.442666:0.627538:0.442666:0.627538:0.426168:0.427973:0.426168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.455594:0.482066:0.485273:0.482066:0.485273:0.465926:0.455594:0.465926:0.000000:0.000000:0.000000
( ):@0.469086:0.485548:0.491686:0.485548:0.491686:0.464487:0.469086:0.464487:0.000000:0.000000:0.000000
=:@0.494329:0.482576:0.504694:0.482576:0.504694:0.466620:0.494329:0.466620:0.000000
f:@0.512189:0.472047:0.516400:0.472047:0.516400:0.455908:0.512189:0.455908:0.000000
2 –:@0.536016:0.471934:0.536025:0.473286:0.536025:0.457119:0.536016:0.455766:0.000000:0.000000:0.000000
+:@0.546060:0.472558:0.556425:0.472558:0.556425:0.456602:0.546060:0.456602:0.000000
h:@0.558521:0.472047:0.567734:0.472047:0.567734:0.455908:0.558521:0.455908:0.000000
(:@0.520134:0.475538:0.526421:0.475538:0.526421:0.454477:0.520134:0.454477:0.000000
):@0.567863:0.475538:0.574150:0.475538:0.574150:0.454477:0.567863:0.454477:0.000000
– –2:@0.575975:0.471940:0.623685:0.471940:0.623685:0.455773:0.575975:0.455773:0.000000:0.000000:0.000000:0.000000
f:@0.591532:0.472054:0.595742:0.472054:0.595742:0.455914:0.591532:0.455914:0.000000
( ):@0.599472:0.475538:0.630567:0.475538:0.630567:0.454477:0.599472:0.454477:0.000000:0.000000:0.000000
h:@0.568463:0.493193:0.577677:0.493193:0.577677:0.477053:0.568463:0.477053:0.000000
–5 + 2  –(–5):@0.651698:0.473288:0.751195:0.473288:0.751195:0.457120:0.651698:0.457120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.697349:0.473401:0.706563:0.473401:0.706563:0.457262:0.697349:0.457262:0.000000
h:@0.702485:0.493197:0.711698:0.493197:0.711698:0.477057:0.702485:0.477057:0.000000
=:@0.634687:0.482576:0.645052:0.482576:0.645052:0.466620:0.634687:0.466620:0.000000
= :@0.756784:0.482576:0.771869:0.482576:0.771869:0.466620:0.756784:0.466620:0.000000:0.000000
2:@0.769452:0.481952:0.777778:0.481952:0.777778:0.465785:0.769452:0.465785:0.000000
Q:@0.455592:0.527536:0.467241:0.527536:0.467241:0.511396:0.455592:0.511396:0.000000
0,02:@0.476058:0.527423:0.506398:0.527423:0.506398:0.511255:0.476058:0.511255:0.000000:0.000000:0.000000:0.000000
(:@0.469086:0.531022:0.475373:0.531022:0.475373:0.509962:0.469086:0.509962:0.000000
):@0.506997:0.531022:0.513284:0.531022:0.513284:0.509962:0.506997:0.509962:0.000000
=:@0.515928:0.528050:0.526293:0.528050:0.526293:0.512095:0.515928:0.512095:0.000000
1:@0.531107:0.518769:0.539433:0.518769:0.539433:0.502601:0.531107:0.502601:0.000000
4:@0.530692:0.538564:0.539018:0.538564:0.539018:0.522396:0.530692:0.522396:0.000000
12 6 0,02:@0.547533:0.527426:0.631171:0.527426:0.631171:0.511259:0.547533:0.511259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.565846:0.528050:0.576211:0.528050:0.576211:0.512095:0.565846:0.512095:0.000000
+:@0.632908:0.528050:0.643273:0.528050:0.643273:0.512095:0.632908:0.512095:0.000000
0,2:@0.651939:0.527426:0.673613:0.527426:0.673613:0.511259:0.651939:0.511259:0.000000:0.000000:0.000000
( ):@0.644958:0.531022:0.680490:0.531022:0.680490:0.509962:0.644958:0.509962:0.000000:0.000000:0.000000
2:@0.680768:0.517279:0.685587:0.517279:0.685587:0.507921:0.680768:0.507921:0.000000
(:@0.541733:0.535882:0.548020:0.535882:0.548020:0.504929:0.541733:0.504929:0.000000
):@0.687845:0.535882:0.694132:0.535882:0.694132:0.504929:0.687845:0.504929:0.000000
=:@0.696775:0.528050:0.707140:0.528050:0.707140:0.512095:0.696775:0.512095:0.000000
3,030:@0.709651:0.527426:0.747826:0.527426:0.747826:0.511259:0.709651:0.511259:0.000000:0.000000:0.000000:0.000000:0.000000
Q:@0.455584:0.572741:0.467232:0.572741:0.467232:0.556602:0.455584:0.556602:0.000000
–0,02:@0.475634:0.572628:0.516188:0.572628:0.516188:0.556460:0.475634:0.556460:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.469086:0.576227:0.475373:0.576227:0.475373:0.555167:0.469086:0.555167:0.000000
):@0.516796:0.576227:0.523083:0.576227:0.523083:0.555167:0.516796:0.555167:0.000000
=:@0.525726:0.573255:0.536091:0.573255:0.536091:0.557300:0.525726:0.557300:0.000000
1:@0.540906:0.563974:0.549232:0.563974:0.549232:0.547806:0.540906:0.547806:0.000000
4:@0.540490:0.583769:0.548816:0.583769:0.548816:0.567601:0.540490:0.567601:0.000000
12 6 0,02:@0.557331:0.572631:0.640969:0.572631:0.640969:0.556464:0.557331:0.556464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.575645:0.573255:0.586010:0.573255:0.586010:0.557300:0.575645:0.557300:0.000000
+:@0.642706:0.573255:0.653071:0.573255:0.653071:0.557300:0.642706:0.557300:0.000000
0,2:@0.661737:0.572631:0.683412:0.572631:0.683412:0.556464:0.661737:0.556464:0.000000:0.000000:0.000000
( ):@0.654757:0.576227:0.690289:0.576227:0.690289:0.555167:0.654757:0.555167:0.000000:0.000000:0.000000
2:@0.690566:0.562484:0.695386:0.562484:0.695386:0.553126:0.690566:0.553126:0.000000
(:@0.551532:0.581087:0.557819:0.581087:0.557819:0.550134:0.551532:0.550134:0.000000
):@0.697644:0.581087:0.703931:0.581087:0.703931:0.550134:0.697644:0.550134:0.000000
=:@0.706573:0.573255:0.716938:0.573255:0.716938:0.557300:0.706573:0.557300:0.000000
2,970:@0.719449:0.572631:0.758040:0.572631:0.758040:0.556464:0.719449:0.556464:0.000000:0.000000:0.000000:0.000000:0.000000
Q:@0.455583:0.610323:0.467232:0.610323:0.467232:0.594183:0.455583:0.594183:0.000000
0,000:@0.476049:0.610210:0.516353:0.610212:0.516353:0.594044:0.476049:0.594042:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.469086:0.613808:0.475373:0.613808:0.475373:0.592747:0.469086:0.592747:0.000000
2:@0.455598:0.649448:0.463924:0.649448:0.463924:0.633280:0.455598:0.633280:0.000000
):@0.464520:0.653045:0.470807:0.653045:0.470807:0.631984:0.464520:0.631984:0.000000
=:@0.473447:0.650072:0.483812:0.650072:0.483812:0.634117:0.473447:0.634117:0.000000
1:@0.488627:0.640791:0.496953:0.640791:0.496953:0.624623:0.488627:0.624623:0.000000
4:@0.488211:0.660586:0.496537:0.660586:0.496537:0.644418:0.488211:0.644418:0.000000
12 6 0,02:@0.505052:0.649449:0.588690:0.649449:0.588690:0.633281:0.505052:0.633281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.523366:0.650072:0.533731:0.650072:0.533731:0.634117:0.523366:0.634117:0.000000
+:@0.590427:0.650072:0.600792:0.650072:0.600792:0.634117:0.590427:0.634117:0.000000
0,02:@0.609458:0.649449:0.639798:0.649449:0.639798:0.633281:0.609458:0.633281:0.000000:0.000000:0.000000:0.000000
(:@0.602477:0.653045:0.608764:0.653045:0.608764:0.631984:0.602477:0.631984:0.000000
):@0.640388:0.653045:0.646675:0.653045:0.646675:0.631984:0.640388:0.631984:0.000000
2:@0.646958:0.639300:0.651777:0.639300:0.651777:0.629942:0.646958:0.629942:0.000000
(:@0.499254:0.657904:0.505541:0.657904:0.505541:0.626951:0.499254:0.626951:0.000000
):@0.654032:0.657904:0.660319:0.657904:0.660319:0.626951:0.654032:0.626951:0.000000
=:@0.662965:0.650072:0.673330:0.650072:0.673330:0.634117:0.662965:0.634117:0.000000
2,970:@0.675841:0.649449:0.714432:0.649449:0.714432:0.633281:0.675841:0.633281:0.000000:0.000000:0.000000:0.000000:0.000000
Q:@0.455588:0.687140:0.467237:0.687140:0.467237:0.671001:0.455588:0.671001:0.000000
–0,000:@0.475638:0.687027:0.526152:0.687028:0.526152:0.670860:0.475638:0.670859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.469086:0.690625:0.475373:0.690625:0.475373:0.669565:0.469086:0.669565:0.000000
2:@0.455598:0.726264:0.463924:0.726264:0.463924:0.710096:0.455598:0.710096:0.000000
):@0.464520:0.729862:0.470807:0.729862:0.470807:0.708801:0.464520:0.708801:0.000000
=:@0.473447:0.726888:0.483812:0.726888:0.483812:0.710933:0.473447:0.710933:0.000000
1:@0.488627:0.717607:0.496953:0.717607:0.496953:0.701439:0.488627:0.701439:0.000000
4:@0.488211:0.737402:0.496537:0.737402:0.496537:0.721234:0.488211:0.721234:0.000000
12–6 0,000:@0.505052:0.726265:0.597356:0.726265:0.597356:0.710097:0.505052:0.710097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.499254:0.729862:0.505541:0.729862:0.505541:0.708801:0.499254:0.708801:0.000000
2:@0.455594:0.763845:0.463920:0.763845:0.463920:0.747678:0.455594:0.747678:0.000000
+:@0.465657:0.764469:0.476022:0.764469:0.476022:0.748514:0.465657:0.748514:0.000000
–0,000:@0.484273:0.763845:0.533077:0.763845:0.533077:0.747678:0.484273:0.747678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.477705:0.767443:0.483992:0.767443:0.483992:0.746382:0.477705:0.746382:0.000000
2:@0.455594:0.799001:0.463920:0.799001:0.463920:0.782833:0.455594:0.782833:0.000000
):@0.464520:0.802597:0.470807:0.802597:0.470807:0.781536:0.464520:0.781536:0.000000
2:@0.471087:0.789123:0.475906:0.789123:0.475906:0.779765:0.471087:0.779765:0.000000
):@0.478168:0.807134:0.484455:0.807134:0.484455:0.776819:0.478168:0.776819:0.000000
=:@0.487095:0.799624:0.497460:0.799624:0.497460:0.783669:0.487095:0.783669:0.000000
2,999:@0.499971:0.799001:0.538562:0.799001:0.538562:0.782833:0.499971:0.782833:0.000000:0.000000:0.000000:0.000000:0.000000
,  h ≠ :@0.781527:0.482314:0.821233:0.482314:0.821233:0.465845:0.781527:0.465845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,:@0.821233:0.482198:0.832484:0.482198:0.832484:0.465701:0.821233:0.465701:0.000000:0.000000
 :@0.404236:0.515483:0.408378:0.515483:0.408378:0.498985:0.404236:0.498985:0.000000
es decir que el cociente incremental es constante y vale 2. :@0.427971:0.515483:0.839569:0.515483:0.839569:0.498985:0.427971:0.498985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.404236:0.550401:0.416508:0.550401:0.416508:0.533687:0.404236:0.533687:0.000000:0.000000
 :@0.416508:0.550647:0.420535:0.550647:0.420535:0.533701:0.416508:0.533701:0.000000
Sean        con   ≠ 0 y   la función real definida por f(x) = :@0.427971:0.550184:0.860607:0.550184:0.860607:0.533687:0.427971:0.533687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.466155:0.549534:0.476866:0.549534:0.476866:0.535234:0.466155:0.535234:0.000000
∈:@0.481394:0.550734:0.495130:0.550734:0.495130:0.531894:0.481394:0.531894:0.000000
R:@0.499657:0.549215:0.513567:0.549215:0.513567:0.535769:0.499657:0.535769:0.000000
:@0.554101:0.549534:0.564812:0.549534:0.564812:0.535234:0.554101:0.535234:0.000000
f:@0.610047:0.550300:0.614343:0.550300:0.614343:0.533831:0.610047:0.533831:0.000000
 :@0.860992:0.549534:0.876520:0.549534:0.876520:0.535234:0.860992:0.535234:0.000000:0.000000
x  :@0.876851:0.550300:0.895912:0.550299:0.895912:0.533830:0.876851:0.533831:0.000000:0.000000:0.000000
3:@0.884310:0.543897:0.889016:0.543897:0.889016:0.534296:0.884310:0.534296:0.000000
, :@0.889015:0.550183:0.895912:0.550183:0.895912:0.533685:0.889015:0.533685:0.000000:0.000000
x:@0.427979:0.570411:0.435453:0.570411:0.435453:0.553942:0.427979:0.553942:0.000000
    . Calculemos el cociente incremental :@0.435453:0.570295:0.751477:0.570295:0.751477:0.553798:0.435453:0.553798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.442312:0.570845:0.456048:0.570845:0.456048:0.552005:0.442312:0.552005:0.000000
R:@0.462906:0.569327:0.476816:0.569327:0.476816:0.555880:0.462906:0.555880:0.000000
Q (h):@0.754193:0.570411:0.793205:0.570411:0.793205:0.553942:0.754193:0.553942:0.000000:0.000000:0.000000:0.000000:0.000000
 para      , :@0.793205:0.570295:0.895893:0.570295:0.895893:0.553798:0.793205:0.553798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.838151:0.570411:0.847553:0.570411:0.847553:0.553942:0.838151:0.553942:0.000000
∈:@0.854492:0.570845:0.868228:0.570845:0.868228:0.552005:0.854492:0.552005:0.000000
R:@0.875087:0.569327:0.888996:0.569327:0.888996:0.555880:0.875087:0.555880:0.000000
 :@0.891751:0.570295:0.895893:0.570295:0.895893:0.553798:0.891751:0.553798:0.000000
tal que  ≠ 0. Sean       y :@0.427959:0.587646:0.631506:0.587646:0.631506:0.571148:0.427959:0.571148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h :@0.482923:0.587762:0.496467:0.587762:0.496467:0.571293:0.482923:0.571293:0.000000:0.000000
a:@0.567960:0.587762:0.576937:0.587762:0.576937:0.571293:0.567960:0.571293:0.000000
∈:@0.581927:0.588196:0.595663:0.588196:0.595663:0.569356:0.581927:0.569356:0.000000
R:@0.600653:0.586677:0.614563:0.586677:0.614563:0.573231:0.600653:0.573231:0.000000
h ≠ :@0.632344:0.587762:0.661753:0.587762:0.661753:0.571293:0.632344:0.571293:0.000000:0.000000:0.000000:0.000000
0. De la definición de la función :@0.662591:0.587646:0.895920:0.587646:0.895920:0.571148:0.662591:0.571148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.891770:0.587646:0.895912:0.587646:0.895912:0.571148:0.891770:0.571148:0.000000
f :@0.427979:0.605113:0.436417:0.605113:0.436417:0.588644:0.427979:0.588644:0.000000:0.000000
y del cociente incremental, se tiene: :@0.436417:0.604997:0.691966:0.604997:0.691966:0.588499:0.436417:0.588499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.405737:0.632705:0.432994:0.632705:0.432994:0.617883:0.405737:0.617883:0.000000:0.000000:0.000000
( ):@0.418129:0.635904:0.438883:0.635904:0.438883:0.616562:0.418129:0.616562:0.000000:0.000000:0.000000
=:@0.441311:0.633174:0.450830:0.633174:0.450830:0.618521:0.441311:0.618521:0.000000
f a h:@0.457713:0.623505:0.500575:0.623505:0.500575:0.608683:0.457713:0.608683:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.480670:0.623974:0.490189:0.623974:0.490189:0.609321:0.480670:0.609321:0.000000
(:@0.465011:0.626710:0.470784:0.626710:0.470784:0.607369:0.465011:0.607369:0.000000
):@0.500676:0.626710:0.506450:0.626710:0.506450:0.607369:0.500676:0.607369:0.000000
–:@0.508121:0.623408:0.517571:0.623408:0.517571:0.608560:0.508121:0.608560:0.000000
f a:@0.522391:0.623512:0.544186:0.623512:0.544186:0.608690:0.522391:0.608690:0.000000:0.000000:0.000000
( ):@0.529700:0.626710:0.550073:0.626710:0.550073:0.607369:0.529700:0.607369:0.000000:0.000000:0.000000
h:@0.498321:0.642925:0.506782:0.642925:0.506782:0.628103:0.498321:0.628103:0.000000
=:@0.553870:0.633174:0.563389:0.633174:0.563389:0.618521:0.553870:0.618521:0.000000
a h:@0.585485:0.623512:0.614632:0.623512:0.614632:0.608690:0.585485:0.608690:0.000000:0.000000:0.000000
+:@0.594727:0.623981:0.604246:0.623981:0.604246:0.609328:0.594727:0.609328:0.000000
(:@0.579078:0.626710:0.584851:0.626710:0.584851:0.607369:0.579078:0.607369:0.000000
):@0.614743:0.626710:0.620517:0.626710:0.620517:0.607369:0.614743:0.607369:0.000000
3:@0.620776:0.614089:0.625202:0.614089:0.625202:0.605495:0.620776:0.605495:0.000000
–:@0.628502:0.623408:0.637952:0.623408:0.637952:0.608560:0.628502:0.608560:0.000000
a:@0.650270:0.623512:0.658350:0.623512:0.658350:0.608690:0.650270:0.608690:0.000000
3:@0.658469:0.616175:0.662895:0.616175:0.662895:0.607581:0.658469:0.607581:0.000000
h:@0.611824:0.642925:0.620285:0.642925:0.620285:0.628103:0.611824:0.628103:0.000000
=:@0.668316:0.633174:0.677835:0.633174:0.677835:0.618521:0.668316:0.618521:0.000000
a:@0.692203:0.624749:0.700283:0.624749:0.700283:0.609927:0.692203:0.609927:0.000000
3:@0.700402:0.617412:0.704828:0.617412:0.704828:0.608818:0.700402:0.608818:0.000000
+:@0.707753:0.625218:0.717272:0.625218:0.717272:0.610565:0.707753:0.610565:0.000000
a h:@0.738068:0.624749:0.759909:0.624749:0.759909:0.609927:0.738068:0.609927:0.000000:0.000000:0.000000
2:@0.746267:0.617412:0.750692:0.617412:0.750692:0.608818:0.746267:0.608818:0.000000
+:@0.761054:0.625218:0.770573:0.625218:0.770573:0.610565:0.761054:0.610565:0.000000
3:@0.772133:0.624645:0.779780:0.624645:0.779780:0.609797:0.772133:0.609797:0.000000
3:@0.719857:0.623409:0.727503:0.623409:0.727503:0.608561:0.719857:0.608561:0.000000
ah:@0.790320:0.624749:0.806705:0.624749:0.806705:0.609927:0.790320:0.609927:0.000000:0.000000
2:@0.806810:0.617412:0.811235:0.617412:0.811235:0.608818:0.806810:0.608818:0.000000
+:@0.814348:0.625218:0.823867:0.625218:0.823867:0.610565:0.814348:0.610565:0.000000
h:@0.836116:0.624749:0.844578:0.624749:0.844578:0.609927:0.836116:0.609927:0.000000
3:@0.844692:0.617412:0.849118:0.617412:0.849118:0.608818:0.844692:0.608818:0.000000
–:@0.852418:0.624645:0.861868:0.624645:0.861868:0.609797:0.852418:0.609797:0.000000
a:@0.874186:0.624749:0.882266:0.624749:0.882266:0.609927:0.874186:0.609927:0.000000
3:@0.882385:0.617412:0.886811:0.617412:0.886811:0.608818:0.882385:0.608818:0.000000
h:@0.781004:0.642925:0.789466:0.642925:0.789466:0.628103:0.781004:0.628103:0.000000
=:@0.405737:0.679851:0.415256:0.679851:0.415256:0.665198:0.405737:0.665198:0.000000
h a:@0.429626:0.668845:0.460749:0.668845:0.460749:0.654023:0.429626:0.654023:0.000000:0.000000:0.000000
3:@0.444797:0.668741:0.452444:0.668741:0.452444:0.653893:0.444797:0.653893:0.000000
3:@0.460864:0.661508:0.465290:0.661508:0.465290:0.652914:0.460864:0.652914:0.000000
+:@0.468214:0.669314:0.477732:0.669314:0.477732:0.654661:0.468214:0.654661:0.000000
3:@0.479293:0.668741:0.486939:0.668741:0.486939:0.653893:0.479293:0.653893:0.000000
ah h:@0.487165:0.668845:0.524599:0.668845:0.524599:0.654023:0.487165:0.654023:0.000000:0.000000:0.000000:0.000000
+:@0.504694:0.669314:0.514213:0.669314:0.514213:0.654661:0.504694:0.654661:0.000000
2:@0.524706:0.661508:0.529132:0.661508:0.529132:0.652914:0.524706:0.652914:0.000000
(:@0.438766:0.673908:0.444540:0.673908:0.444540:0.650610:0.438766:0.650610:0.000000
):@0.531216:0.673908:0.536990:0.673908:0.536990:0.650610:0.531216:0.650610:0.000000
h:@0.473961:0.689602:0.482423:0.689602:0.482423:0.674780:0.473961:0.674780:0.000000
=:@0.540773:0.679851:0.550292:0.679851:0.550292:0.665198:0.540773:0.665198:0.000000
3:@0.570644:0.679279:0.578291:0.679279:0.578291:0.664431:0.570644:0.664431:0.000000
a:@0.578516:0.679383:0.586596:0.679383:0.586596:0.664561:0.578516:0.664561:0.000000
2:@0.586712:0.672046:0.591137:0.672046:0.591137:0.663452:0.586712:0.663452:0.000000
+:@0.594250:0.679851:0.603769:0.679851:0.603769:0.665198:0.594250:0.665198:0.000000
3:@0.605330:0.679279:0.612976:0.679279:0.612976:0.664431:0.605330:0.664431:0.000000
ah h:@0.613201:0.679383:0.650636:0.679383:0.650636:0.664561:0.613201:0.664561:0.000000:0.000000:0.000000:0.000000
+:@0.630731:0.679851:0.640250:0.679851:0.640250:0.665198:0.630731:0.665198:0.000000
2:@0.650741:0.672046:0.655167:0.672046:0.655167:0.663452:0.650741:0.663452:0.000000
(:@0.564614:0.684445:0.570387:0.684445:0.570387:0.661147:0.564614:0.661147:0.000000
):@0.657237:0.684445:0.663011:0.684445:0.663011:0.661147:0.657237:0.661147:0.000000
h:@0.681311:0.679383:0.689772:0.679383:0.689772:0.664561:0.681311:0.664561:0.000000
0.:@0.704258:0.679279:0.714315:0.679279:0.714315:0.664431:0.704258:0.664431:0.000000:0.000000
,:@0.664067:0.679279:0.666546:0.679279:0.666546:0.664431:0.664067:0.664431:0.000000
=:@0.419355:0.721614:0.428874:0.721614:0.428874:0.706961:0.419355:0.706961:0.000000
1:@0.433296:0.713090:0.440942:0.713090:0.440942:0.698242:0.433296:0.698242:0.000000
4:@0.432914:0.731269:0.440560:0.731269:0.440560:0.716421:0.432914:0.716421:0.000000
Para:@0.427971:0.714531:0.458314:0.714531:0.458314:0.698033:0.427971:0.698033:0.000000:0.000000:0.000000:0.000000
Q h:@0.464964:0.617659:0.494469:0.617659:0.494469:0.601614:0.464964:0.601614:0.000000:0.000000:0.000000
( ):@0.478377:0.621122:0.500844:0.621122:0.500844:0.600184:0.478377:0.600184:0.000000:0.000000:0.000000
=:@0.503471:0.618166:0.513775:0.618166:0.513775:0.602304:0.503471:0.602304:0.000000
f a h:@0.521227:0.607699:0.567624:0.607699:0.567624:0.591655:0.521227:0.591655:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.546077:0.608207:0.556382:0.608207:0.556382:0.592345:0.546077:0.592345:0.000000
(:@0.529125:0.611169:0.535375:0.611169:0.535375:0.590231:0.529125:0.590231:0.000000
):@0.567734:0.611169:0.573984:0.611169:0.573984:0.590231:0.567734:0.590231:0.000000
–:@0.575794:0.607593:0.586023:0.607593:0.586023:0.591520:0.575794:0.591520:0.000000
f a:@0.591241:0.607706:0.614834:0.607706:0.614834:0.591661:0.591241:0.591661:0.000000:0.000000:0.000000
( ):@0.599154:0.611169:0.621208:0.611169:0.621208:0.590231:0.599154:0.590231:0.000000:0.000000:0.000000
h:@0.565185:0.628722:0.574344:0.628722:0.574344:0.612677:0.565185:0.612677:0.000000
=:@0.625322:0.618171:0.635626:0.618171:0.635626:0.602309:0.625322:0.602309:0.000000
a h:@0.659543:0.607706:0.691094:0.607706:0.691094:0.591661:0.659543:0.591661:0.000000:0.000000:0.000000
+:@0.669547:0.608213:0.679851:0.608213:0.679851:0.592351:0.669547:0.592351:0.000000
(:@0.652606:0.611169:0.658856:0.611169:0.658856:0.590231:0.652606:0.590231:0.000000
):@0.691214:0.611169:0.697464:0.611169:0.697464:0.590231:0.691214:0.590231:0.000000
3:@0.697745:0.597505:0.702536:0.597505:0.702536:0.588202:0.697745:0.588202:0.000000
–:@0.706109:0.607593:0.716339:0.607593:0.716339:0.591520:0.706109:0.591520:0.000000
a:@0.729673:0.607706:0.738420:0.607706:0.738420:0.591661:0.729673:0.591661:0.000000
3:@0.738547:0.599765:0.743338:0.599765:0.743338:0.590462:0.738547:0.590462:0.000000
h:@0.688054:0.628722:0.697213:0.628722:0.697213:0.612677:0.688054:0.612677:0.000000
=:@0.749204:0.618171:0.759509:0.618171:0.759509:0.602309:0.749204:0.602309:0.000000
a:@0.775066:0.609046:0.783812:0.609046:0.783812:0.593001:0.775066:0.593001:0.000000
3:@0.783941:0.601104:0.788732:0.601104:0.788732:0.591801:0.783941:0.591801:0.000000
+:@0.791897:0.609553:0.802201:0.609553:0.802201:0.593692:0.791897:0.593692:0.000000
a h:@0.824715:0.609046:0.848358:0.609046:0.848358:0.593001:0.824715:0.593001:0.000000:0.000000:0.000000
2:@0.833588:0.601104:0.838379:0.601104:0.838379:0.591801:0.833588:0.591801:0.000000
+:@0.849597:0.609553:0.859901:0.609553:0.859901:0.593692:0.849597:0.593692:0.000000
3:@0.861591:0.608934:0.869868:0.608934:0.869868:0.592861:0.861591:0.592861:0.000000
3:@0.805001:0.607595:0.813278:0.607595:0.813278:0.591522:0.805001:0.591522:0.000000
ah:@0.881277:0.609046:0.899015:0.609046:0.899015:0.593001:0.881277:0.593001:0.000000:0.000000
2:@0.899129:0.601104:0.903920:0.601104:0.903920:0.591801:0.899129:0.591801:0.000000
+:@0.907289:0.609553:0.917593:0.609553:0.917593:0.593692:0.907289:0.593692:0.000000
h:@0.930853:0.609046:0.940012:0.609046:0.940012:0.593001:0.930853:0.593001:0.000000
3:@0.940135:0.601104:0.944926:0.601104:0.944926:0.591801:0.940135:0.591801:0.000000
–:@0.948500:0.608934:0.958729:0.608934:0.958729:0.592861:0.948500:0.592861:0.000000
a:@0.972064:0.609046:0.980810:0.609046:0.980810:0.593001:0.972064:0.593001:0.000000
3:@0.980939:0.601104:0.985730:0.601104:0.985730:0.591801:0.980939:0.591801:0.000000
h:@0.871192:0.628722:0.880352:0.628722:0.880352:0.612677:0.871192:0.612677:0.000000
=:@0.464967:0.668700:0.475271:0.668700:0.475271:0.652838:0.464967:0.652838:0.000000
h a:@0.490823:0.656780:0.524514:0.656780:0.524514:0.640735:0.490823:0.640735:0.000000:0.000000:0.000000
3:@0.507246:0.656667:0.515523:0.656667:0.515523:0.640594:0.507246:0.640594:0.000000
3:@0.524637:0.648838:0.529428:0.648838:0.529428:0.639535:0.524637:0.639535:0.000000
+:@0.532595:0.657287:0.542899:0.657287:0.542899:0.641425:0.532595:0.641425:0.000000
3:@0.544588:0.656667:0.552866:0.656667:0.552866:0.640594:0.544588:0.640594:0.000000
ah h:@0.553110:0.656780:0.593633:0.656780:0.593633:0.640735:0.553110:0.640735:0.000000:0.000000:0.000000:0.000000
+:@0.572085:0.657287:0.582390:0.657287:0.582390:0.641425:0.572085:0.641425:0.000000
2:@0.593748:0.648838:0.598539:0.648838:0.598539:0.639535:0.593748:0.639535:0.000000
(:@0.500717:0.662260:0.506967:0.662260:0.506967:0.637040:0.500717:0.637040:0.000000
):@0.600795:0.662260:0.607045:0.662260:0.607045:0.637040:0.600795:0.637040:0.000000
h:@0.538817:0.679250:0.547976:0.679250:0.547976:0.663205:0.538817:0.663205:0.000000
=:@0.611135:0.668699:0.621439:0.668699:0.621439:0.652837:0.611135:0.652837:0.000000
3:@0.643477:0.668074:0.651755:0.668074:0.651755:0.652001:0.643477:0.652001:0.000000
a:@0.651998:0.668187:0.660745:0.668187:0.660745:0.652142:0.651998:0.652142:0.000000
2:@0.660868:0.660246:0.665659:0.660246:0.665659:0.650943:0.660868:0.650943:0.000000
+:@0.669030:0.668694:0.679334:0.668694:0.679334:0.652833:0.669030:0.652833:0.000000
3:@0.681023:0.668074:0.689300:0.668074:0.689300:0.652001:0.681023:0.652001:0.000000
ah h:@0.689545:0.668187:0.730068:0.668187:0.730068:0.652142:0.689545:0.652142:0.000000:0.000000:0.000000:0.000000
+:@0.708520:0.668694:0.718825:0.668694:0.718825:0.652833:0.708520:0.652833:0.000000
2:@0.730183:0.660246:0.734973:0.660246:0.734973:0.650943:0.730183:0.650943:0.000000
(:@0.636949:0.673668:0.643199:0.673668:0.643199:0.648447:0.636949:0.648447:0.000000
):@0.737215:0.673668:0.743465:0.673668:0.743465:0.648447:0.737215:0.648447:0.000000
h:@0.763275:0.668187:0.772435:0.668187:0.772435:0.652142:0.763275:0.652142:0.000000
0.:@0.788107:0.668074:0.798993:0.668074:0.798993:0.652001:0.788107:0.652001:0.000000:0.000000
,:@0.744600:0.668074:0.747284:0.668074:0.747284:0.652001:0.744600:0.652001:0.000000
=:@0.479704:0.713903:0.490008:0.713903:0.490008:0.698041:0.479704:0.698041:0.000000
1:@0.494795:0.704676:0.503072:0.704676:0.503072:0.688603:0.494795:0.688603:0.000000
4:@0.494382:0.724355:0.502659:0.724355:0.502659:0.708282:0.494382:0.708282:0.000000
 y   = 2, se tiene :@0.509951:0.714531:0.627931:0.714531:0.627931:0.698033:0.509951:0.698033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.526056:0.714647:0.535034:0.714647:0.535034:0.698178:0.526056:0.698178:0.000000
(:@0.795235:0.717943:0.800804:0.717943:0.800804:0.694908:0.795235:0.694908:0.000000
):@0.875367:0.717943:0.880935:0.717943:0.880935:0.694908:0.875367:0.694908:0.000000
():@0.642169:0.716107:0.662887:0.716107:0.662887:0.697030:0.642169:0.697030:0.000000:0.000000
=:@0.665684:0.714140:0.674864:0.714140:0.674864:0.700009:0.665684:0.700009:0.000000
+:@0.703258:0.706008:0.712439:0.706008:0.712439:0.691876:0.703258:0.691876:0.000000
=:@0.771751:0.714140:0.780932:0.714140:0.780932:0.700009:0.771751:0.700009:0.000000
+:@0.818004:0.714140:0.827184:0.714140:0.827184:0.700009:0.818004:0.700009:0.000000
+:@0.848304:0.714140:0.857484:0.714140:0.857484:0.700009:0.848304:0.700009:0.000000
(2:@0.688493:0.705455:0.700650:0.705455:0.700650:0.691136:0.688493:0.691136:0.000000:0.000000
)– (2):@0.722890:0.705455:0.767604:0.705455:0.767604:0.691136:0.722890:0.691136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.785948:0.705455:0.793322:0.705455:0.793322:0.691136:0.785948:0.691136:0.000000
4:@0.785597:0.723101:0.792971:0.723101:0.792971:0.708781:0.785597:0.708781:0.000000
12 6:@0.800713:0.713588:0.837446:0.713588:0.837446:0.699268:0.800713:0.699268:0.000000:0.000000:0.000000:0.000000
,:@0.882629:0.713588:0.885020:0.713588:0.885020:0.699268:0.882629:0.699268:0.000000
2:@0.868611:0.706616:0.872874:0.706616:0.872874:0.698338:0.868611:0.698338:0.000000
Qh:@0.630020:0.713688:0.656859:0.713688:0.656859:0.699394:0.630020:0.699394:0.000000:0.000000
f:@0.682326:0.705556:0.686055:0.705556:0.686055:0.691261:0.682326:0.691261:0.000000
h:@0.715335:0.705556:0.723495:0.705556:0.723495:0.691261:0.715335:0.691261:0.000000
f:@0.744247:0.705556:0.747976:0.705556:0.747976:0.691261:0.744247:0.691261:0.000000
h:@0.719599:0.723201:0.727759:0.723201:0.727759:0.708907:0.719599:0.708907:0.000000
hh:@0.838007:0.713688:0.868558:0.713688:0.868558:0.699394:0.838007:0.699394:0.000000:0.000000
 :@0.404236:0.751999:0.408378:0.751999:0.408378:0.735501:0.404236:0.735501:0.000000
h :@0.427971:0.752114:0.441514:0.752114:0.441514:0.735646:0.427971:0.735646:0.000000:0.000000
≠ 0. Calculemos algunos valores de este cociente: :@0.441514:0.751999:0.793080:0.751999:0.793080:0.735501:0.441514:0.735501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q:@0.411517:0.779502:0.423003:0.779502:0.423003:0.763589:0.411517:0.763589:0.000000
Q:@0.745090:0.779502:0.756575:0.779502:0.756575:0.763589:0.745090:0.763589:0.000000
Q:@0.411517:0.809156:0.423003:0.809156:0.423003:0.793242:0.411517:0.793242:0.000000
Q:@0.607372:0.809156:0.618857:0.809156:0.618857:0.793242:0.607372:0.793242:0.000000
0,02:@0.431920:0.779396:0.462077:0.779396:0.462077:0.763455:0.431920:0.763455:0.000000:0.000000:0.000000:0.000000
1:@0.487804:0.770343:0.496013:0.770343:0.496013:0.754402:0.487804:0.754402:0.000000
4:@0.487413:0.789987:0.495622:0.789987:0.495622:0.774046:0.487413:0.774046:0.000000
1260,02:@0.504241:0.779396:0.591604:0.779396:0.591604:0.763455:0.504241:0.763455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,02:@0.614427:0.779396:0.644584:0.779396:0.644584:0.763455:0.614427:0.763455:0.000000:0.000000:0.000000:0.000000
3,030 1,:@0.681648:0.779396:0.733231:0.779396:0.733231:0.763455:0.681648:0.763455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–0,02:@0.765101:0.779396:0.805348:0.779396:0.805348:0.763455:0.765101:0.763455:0.000000:0.000000:0.000000:0.000000:0.000000
2,970 1.:@0.828841:0.779396:0.881300:0.779396:0.881300:0.763455:0.828841:0.763455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,000 2:@0.431920:0.809044:0.482535:0.809044:0.482535:0.793102:0.431920:0.793102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3,000 300 01,:@0.506028:0.809044:0.595513:0.809044:0.595513:0.793102:0.506028:0.793102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–0,000 2:@0.627365:0.809044:0.688070:0.809044:0.688070:0.793102:0.627365:0.793102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,999 700 01.:@0.711563:0.809044:0.801904:0.809044:0.801904:0.793102:0.711563:0.793102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.651676:0.769665:0.656422:0.769665:0.656422:0.760449:0.651676:0.760449:0.000000
(:@0.498147:0.786781:0.504346:0.786781:0.504346:0.755947:0.498147:0.755947:0.000000
):@0.659190:0.786781:0.665389:0.786781:0.665389:0.755947:0.659190:0.755947:0.000000
(:@0.424654:0.782195:0.430853:0.782195:0.430853:0.760957:0.424654:0.760957:0.000000
):@0.463095:0.782195:0.469294:0.782195:0.469294:0.760957:0.463095:0.760957:0.000000
(:@0.607180:0.782195:0.613379:0.782195:0.613379:0.760957:0.607180:0.760957:0.000000
):@0.645621:0.782195:0.651820:0.782195:0.651820:0.760957:0.645621:0.760957:0.000000
(:@0.758245:0.782195:0.764445:0.782195:0.764445:0.760957:0.758245:0.760957:0.000000
):@0.806386:0.782195:0.812584:0.782195:0.812584:0.760957:0.806386:0.760957:0.000000
(:@0.424673:0.811845:0.430872:0.811845:0.430872:0.790607:0.424673:0.790607:0.000000
):@0.483572:0.811845:0.489771:0.811845:0.489771:0.790607:0.483572:0.790607:0.000000
(:@0.620527:0.811845:0.626726:0.811845:0.626726:0.790607:0.620527:0.790607:0.000000
):@0.689126:0.811845:0.695325:0.811845:0.695325:0.790607:0.689126:0.790607:0.000000
=:@0.472016:0.780005:0.482236:0.780005:0.482236:0.764273:0.472016:0.764273:0.000000
+ ×:@0.523507:0.780005:0.558244:0.780005:0.558244:0.764273:0.523507:0.764273:0.000000:0.000000:0.000000
+:@0.594507:0.780005:0.604727:0.780005:0.604727:0.764273:0.594507:0.764273:0.000000
=:@0.668110:0.780005:0.678330:0.780005:0.678330:0.764273:0.668110:0.764273:0.000000
=:@0.815285:0.780005:0.825505:0.780005:0.825505:0.764273:0.815285:0.764273:0.000000
=:@0.492472:0.809652:0.502692:0.809652:0.502692:0.793921:0.492472:0.793921:0.000000
=:@0.698025:0.809652:0.708245:0.809652:0.708245:0.793921:0.698025:0.793921:0.000000
 :@0.404236:0.840574:0.408378:0.840574:0.408378:0.824077:0.404236:0.824077:0.000000
Para valores de   no nulos y cada vez más próximos a 0, el cociente :@0.427971:0.840574:0.895990:0.840574:0.895990:0.824077:0.427971:0.824077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.535384:0.840690:0.544786:0.840690:0.544786:0.824221:0.535384:0.824221:0.000000
incremental se aproxima cada vez a 3. Calculemos la distancia de :@0.427971:0.857925:0.895922:0.857925:0.895922:0.841427:0.427971:0.841427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.891780:0.857925:0.895922:0.857925:0.895922:0.841427:0.891780:0.841427:0.000000
 :@0.891780:0.857925:0.895922:0.857925:0.895922:0.841427:0.891780:0.841427:0.000000
3 a :@0.427971:0.875276:0.452592:0.875276:0.452592:0.858778:0.427971:0.858778:0.000000:0.000000:0.000000:0.000000
Q(h):@0.452592:0.875391:0.484746:0.875391:0.484746:0.858923:0.452592:0.858923:0.000000:0.000000:0.000000:0.000000
, esto es, d(3, Q(h)),     ≠ 0. Tenemos: :@0.484746:0.875276:0.750200:0.875276:0.750200:0.858778:0.484746:0.858778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.634454:0.875391:0.643856:0.875391:0.643856:0.858923:0.634454:0.858923:0.000000
(:@0.620866:0.907682:0.627360:0.907682:0.627360:0.880821:0.620866:0.880821:0.000000
):@0.714309:0.907682:0.720803:0.907682:0.720803:0.880821:0.714309:0.880821:0.000000
(:@0.417997:0.905541:0.424490:0.905541:0.424490:0.883295:0.417997:0.883295:0.000000
):@0.473395:0.905541:0.479889:0.905541:0.479889:0.883295:0.473395:0.883295:0.000000
():@0.524894:0.905541:0.549055:0.905541:0.549055:0.883295:0.524894:0.883295:0.000000:0.000000
=:@0.483148:0.903248:0.493854:0.903248:0.493854:0.886769:0.483148:0.886769:0.000000
=:@0.580140:0.903248:0.590846:0.903248:0.590846:0.886769:0.580140:0.886769:0.000000
+:@0.647415:0.903248:0.658120:0.903248:0.658120:0.886769:0.647415:0.886769:0.000000
+:@0.682768:0.903248:0.693473:0.903248:0.693473:0.886769:0.682768:0.886769:0.000000
=:@0.748677:0.903248:0.759382:0.903248:0.759382:0.886769:0.748677:0.886769:0.000000
+:@0.789861:0.903248:0.800566:0.903248:0.800566:0.886769:0.789861:0.886769:0.000000
≠:@0.875367:0.903248:0.886072:0.903248:0.886072:0.886769:0.875367:0.886769:0.000000
3, ():@0.425195:0.902604:0.472599:0.902604:0.472599:0.885906:0.425195:0.885906:0.000000:0.000000:0.000000:0.000000:0.000000
–3:@0.551339:0.902604:0.572789:0.902604:0.572789:0.885906:0.551339:0.885906:0.000000:0.000000
1:@0.610034:0.893121:0.618633:0.893121:0.618633:0.876422:0.610034:0.876422:0.000000
4:@0.609644:0.913695:0.618243:0.913695:0.618243:0.896996:0.609644:0.896996:0.000000
12 6:@0.627264:0.902604:0.670086:0.902604:0.670086:0.885906:0.627264:0.885906:0.000000:0.000000:0.000000:0.000000
–3:@0.722677:0.902604:0.744126:0.902604:0.744126:0.885906:0.722677:0.885906:0.000000:0.000000
3:@0.765986:0.893121:0.774585:0.893121:0.774585:0.876422:0.765986:0.876422:0.000000
2:@0.765795:0.913695:0.774394:0.913695:0.774394:0.896996:0.765795:0.896996:0.000000
1:@0.805860:0.893114:0.814459:0.893114:0.814459:0.876415:0.805860:0.876415:0.000000
4:@0.805454:0.913695:0.814054:0.913695:0.814054:0.896996:0.805454:0.896996:0.000000
,:@0.849992:0.902601:0.852780:0.902601:0.852780:0.885903:0.849992:0.885903:0.000000
0.:@0.890005:0.902601:0.901324:0.902604:0.901324:0.885906:0.890005:0.885903:0.000000:0.000000
2:@0.706431:0.894474:0.711403:0.894474:0.711403:0.884820:0.706431:0.884820:0.000000
2:@0.827090:0.894474:0.832061:0.894474:0.832061:0.884820:0.827090:0.884820:0.000000
d:@0.407079:0.902721:0.416361:0.902721:0.416361:0.886052:0.407079:0.886052:0.000000
Q h:@0.438864:0.902721:0.467275:0.902721:0.467275:0.886052:0.438864:0.886052:0.000000:0.000000:0.000000
Q h:@0.510720:0.902721:0.542018:0.902721:0.542018:0.886052:0.510720:0.886052:0.000000:0.000000:0.000000
h h:@0.670736:0.902721:0.706342:0.902721:0.706342:0.886052:0.670736:0.886052:0.000000:0.000000:0.000000
h:@0.777829:0.902721:0.787344:0.902721:0.787344:0.886052:0.777829:0.886052:0.000000
h:@0.817489:0.902721:0.827005:0.902721:0.827005:0.886052:0.817489:0.886052:0.000000
h:@0.862787:0.902721:0.872303:0.902721:0.872303:0.886052:0.862787:0.886052:0.000000
Desequilibrio cognitivo:@0.199646:0.188680:0.363493:0.188680:0.363493:0.173208:0.199646:0.173208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo interpretas de :@0.199884:0.217308:0.343645:0.217308:0.343645:0.202244:0.199884:0.202244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
manera geométrica la tangente :@0.153341:0.233149:0.359300:0.233149:0.359300:0.218086:0.153341:0.218086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a una curva?:@0.153341:0.248991:0.233920:0.248991:0.233920:0.233928:0.153341:0.233928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.100622:0.307805:0.100622:0.307805:0.085150:0.199646:0.085150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es una cantidad :@0.199884:0.129250:0.343770:0.129250:0.343770:0.114187:0.199884:0.114187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
suficientemente pequeña?:@0.153341:0.145092:0.323503:0.145092:0.323503:0.130029:0.153341:0.130029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia digital:@0.199646:0.693581:0.341998:0.693581:0.341998:0.678108:0.199646:0.678108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para profundizar sobre :@0.199884:0.722208:0.350525:0.722208:0.350525:0.707145:0.199884:0.707145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el estudio de valor absoluto :@0.153341:0.738050:0.336168:0.738050:0.336168:0.722987:0.153341:0.722987:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y distancia entre dos puntos, :@0.153341:0.753892:0.342432:0.753892:0.342432:0.738829:0.153341:0.738829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
visita:@0.153341:0.770157:0.190524:0.770157:0.190524:0.754684:0.153341:0.754684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la siguiente página::@0.190526:0.769734:0.315783:0.769734:0.315783:0.754671:0.190526:0.754671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lynk.ec/11m10:@0.153341:0.793035:0.251229:0.793035:0.251229:0.777721:0.153341:0.777721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática e Historia:@0.199880:0.353036:0.355549:0.353036:0.355549:0.337563:0.199880:0.337563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los trabajos de Leibniz que :@0.153337:0.375584:0.331804:0.375584:0.331804:0.360521:0.153337:0.360521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
buscaban un método general :@0.153337:0.391426:0.348038:0.391426:0.348038:0.376363:0.153337:0.376363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para hallar la tangente a una :@0.153337:0.407268:0.339967:0.407268:0.339967:0.392205:0.153337:0.392205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
curva dieron origen a la noción :@0.153337:0.423110:0.358769:0.423110:0.358769:0.408047:0.153337:0.408047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de derivada como el cociente :@0.153337:0.438952:0.348162:0.438952:0.348162:0.423889:0.153337:0.423889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incremental o el cociente de :@0.153337:0.454794:0.341021:0.454794:0.341021:0.439731:0.153337:0.439731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diferencias de una función :@0.153337:0.470636:0.327934:0.470636:0.327934:0.455573:0.153337:0.455573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y = f  x .:@0.153337:0.486584:0.205861:0.486584:0.205861:0.471547:0.153337:0.471547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.185562:0.486478:0.203258:0.486478:0.203258:0.471415:0.185562:0.471415:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.199644:0.323986:0.346429:0.323986:0.346429:0.308513:0.199644:0.308513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.305394:0.525583:0.308415:0.525583:0.308415:0.507487:0.305394:0.507487:0.000000
,:@0.358392:0.525583:0.361414:0.525583:0.361414:0.507487:0.358392:0.507487:0.000000
lím:@0.199790:0.572543:0.224028:0.572543:0.224028:0.554447:0.199790:0.554447:0.000000:0.000000:0.000000
():@0.240955:0.562757:0.269229:0.562757:0.269229:0.544661:0.240955:0.544661:0.000000:0.000000
():@0.297461:0.562757:0.320051:0.562757:0.320051:0.544661:0.297461:0.544661:0.000000:0.000000
.:@0.323495:0.572543:0.326517:0.572543:0.326517:0.554447:0.323495:0.554447:0.000000
1:@0.232424:0.516650:0.237811:0.516650:0.237811:0.506188:0.232424:0.506188:0.000000
1:@0.239803:0.540562:0.245190:0.540562:0.245190:0.530101:0.239803:0.530101:0.000000
1:@0.322511:0.528047:0.327898:0.528047:0.327898:0.517585:0.322511:0.517585:0.000000
1:@0.256747:0.565218:0.262135:0.565218:0.262135:0.554756:0.256747:0.554756:0.000000
1:@0.262795:0.587517:0.268182:0.587517:0.268182:0.577055:0.262795:0.577055:0.000000
1:@0.203313:0.581800:0.207220:0.581800:0.207220:0.574213:0.203313:0.574213:0.000000
y:@0.171999:0.515922:0.180431:0.515922:0.180431:0.497857:0.171999:0.497857:0.000000
x:@0.171788:0.538221:0.179987:0.538221:0.179987:0.520156:0.171788:0.520156:0.000000
fx:@0.206127:0.514304:0.232204:0.514304:0.232204:0.496239:0.206127:0.496239:0.000000:0.000000
fx:@0.266670:0.514304:0.292746:0.514304:0.292746:0.496239:0.266670:0.496239:0.000000:0.000000
x:@0.231401:0.538221:0.239600:0.538221:0.239600:0.520156:0.231401:0.520156:0.000000
x:@0.264028:0.538221:0.272228:0.538221:0.272228:0.520156:0.264028:0.520156:0.000000
x:@0.314088:0.525710:0.322287:0.525710:0.322287:0.507645:0.314088:0.507645:0.000000
x:@0.347941:0.525710:0.356141:0.525710:0.356141:0.507645:0.347941:0.507645:0.000000
dy:@0.159343:0.562882:0.177453:0.562882:0.177453:0.544817:0.159343:0.544817:0.000000:0.000000
dx:@0.159343:0.585181:0.177220:0.585181:0.177220:0.567116:0.159343:0.567116:0.000000:0.000000
fx:@0.233135:0.562882:0.256528:0.562882:0.256528:0.544817:0.233135:0.544817:0.000000:0.000000
fx:@0.289642:0.562882:0.313035:0.562882:0.313035:0.544817:0.289642:0.544817:0.000000:0.000000
x:@0.254373:0.585181:0.262572:0.585181:0.262572:0.567116:0.254373:0.567116:0.000000
x:@0.287000:0.585181:0.295199:0.585181:0.295199:0.567116:0.287000:0.567116:0.000000
x:@0.198634:0.580080:0.203374:0.580080:0.203374:0.569636:0.198634:0.569636:0.000000
x:@0.220588:0.580080:0.225328:0.580080:0.225328:0.569636:0.220588:0.569636:0.000000
():@0.215309:0.518216:0.246289:0.518216:0.246289:0.494643:0.215309:0.494643:0.000000:0.000000
():@0.275852:0.518216:0.301168:0.518216:0.301168:0.494643:0.275852:0.494643:0.000000:0.000000
=:@0.185978:0.526281:0.197579:0.526281:0.197579:0.508422:0.185978:0.508422:0.000000
−:@0.248760:0.514877:0.260362:0.514877:0.260362:0.497019:0.248760:0.497019:0.000000
−:@0.248760:0.538794:0.260362:0.538794:0.260362:0.520936:0.248760:0.520936:0.000000
≠:@0.332083:0.526281:0.343684:0.526281:0.343684:0.508422:0.332083:0.508422:0.000000
=:@0.182998:0.573242:0.194599:0.573242:0.194599:0.555383:0.182998:0.555383:0.000000
−:@0.271773:0.563456:0.283374:0.563456:0.283374:0.545598:0.271773:0.545598:0.000000
−:@0.271773:0.585755:0.283374:0.585755:0.283374:0.567897:0.271773:0.567897:0.000000
→:@0.207990:0.580410:0.220048:0.580410:0.220048:0.570085:0.207990:0.570085:0.000000