196:@0.026565:0.967627:0.050760:0.967627:0.050760:0.951847:0.026565:0.951847:0.000000:0.000000:0.000000
Interpretación geométrica  :@0.404235:0.118449:0.748446:0.118449:0.748446:0.073790:0.404235:0.073790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y física del cociente incremental :@0.404235:0.156168:0.810514:0.156168:0.810514:0.111509:0.404235:0.111509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.34. Interpretar de manera geométrica (pendiente de la secante) y física el cociente incremental (velocidad media) de funciones cuadráticas, con apoyo de las TIC.:@0.143849:0.951654:0.864527:0.951654:0.864527:0.941612:0.143849:0.941612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.404236:0.187186:0.442035:0.187186:0.442035:0.170689:0.404236:0.170689:0.000000:0.000000:0.000000:0.000000:0.000000
A, B :@0.442998:0.187302:0.475941:0.187302:0.475941:0.170833:0.442998:0.170833:0.000000:0.000000:0.000000:0.000000:0.000000
dos intervalos de  ,  una función de  en  ,      fijo y :@0.476905:0.187186:0.895847:0.187186:0.895847:0.170689:0.476905:0.170689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.604631:0.186218:0.618541:0.186218:0.618541:0.172771:0.604631:0.172771:0.000000
f :@0.626442:0.187302:0.634880:0.187302:0.634880:0.170833:0.626442:0.170833:0.000000:0.000000
A :@0.750953:0.187302:0.766365:0.187302:0.766365:0.170833:0.750953:0.170833:0.000000:0.000000
B a:@0.790004:0.187302:0.816031:0.187302:0.816031:0.170833:0.790004:0.170833:0.000000:0.000000:0.000000
∈:@0.821136:0.187736:0.834872:0.187736:0.834872:0.168896:0.821136:0.168896:0.000000
A :@0.839978:0.187302:0.855390:0.187302:0.855390:0.170833:0.839978:0.170833:0.000000:0.000000
 :@0.891705:0.187186:0.895847:0.187186:0.895847:0.170689:0.891705:0.170689:0.000000
h   :@0.404178:0.204653:0.434849:0.204653:0.434849:0.188184:0.404178:0.188184:0.000000:0.000000:0.000000:0.000000
∈:@0.416971:0.205087:0.430707:0.205087:0.430707:0.186247:0.416971:0.186247:0.000000
R:@0.434097:0.203568:0.448007:0.203568:0.448007:0.190122:0.434097:0.190122:0.000000
, tal que :@0.448007:0.204537:0.506689:0.204537:0.506689:0.188039:0.448007:0.188039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h ≠ :@0.505937:0.204653:0.533756:0.204653:0.533756:0.188184:0.505937:0.188184:0.000000:0.000000:0.000000:0.000000
0, y   + :@0.533005:0.204537:0.586177:0.204537:0.586177:0.188039:0.533005:0.188039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a h   A:@0.558859:0.204653:0.626673:0.204653:0.626673:0.188184:0.558859:0.188184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.598276:0.205087:0.612012:0.205087:0.612012:0.186247:0.598276:0.186247:0.000000
.  El grafo de la función  es el conjunto :@0.626673:0.204537:0.895826:0.204537:0.895826:0.188039:0.626673:0.188039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.785727:0.204653:0.794165:0.204653:0.794165:0.188184:0.785727:0.188184:0.000000:0.000000
definido como  ( ) = {(:@0.404159:0.221888:0.572535:0.221888:0.572535:0.205390:0.404159:0.205390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G f:@0.513988:0.222004:0.535681:0.222004:0.535681:0.205535:0.513988:0.205535:0.000000:0.000000:0.000000
x, f (x) x   A:@0.572535:0.222004:0.665625:0.222004:0.665625:0.205535:0.572535:0.205535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)|:@0.613898:0.221888:0.624860:0.221888:0.624860:0.205390:0.613898:0.205390:0.000000:0.000000
∈:@0.636477:0.222437:0.650213:0.222437:0.650213:0.203597:0.636477:0.203597:0.000000
}. :@0.665625:0.221888:0.678379:0.221888:0.678379:0.205390:0.665625:0.205390:0.000000:0.000000:0.000000
La representación gráfica de  ( ) en el sistema de coordenadas rec-:@0.404159:0.256589:0.891686:0.256589:0.891686:0.240092:0.404159:0.240092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G f:@0.613376:0.256705:0.635069:0.256705:0.635069:0.240236:0.613376:0.240236:0.000000:0.000000:0.000000
tangulares se llama gráfica de la función  o representación gráfica de :@0.404159:0.273940:0.895864:0.273940:0.895864:0.257442:0.404159:0.257442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.690653:0.274056:0.699091:0.274056:0.699091:0.257587:0.690653:0.257587:0.000000:0.000000
la función .:@0.404159:0.291291:0.486131:0.291291:0.486131:0.274793:0.404159:0.274793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 f:@0.474938:0.291407:0.483376:0.291407:0.483376:0.274938:0.474938:0.274938:0.000000:0.000000
Consideramos dos puntos del grafo de :@0.404159:0.325992:0.682037:0.325992:0.682037:0.309495:0.404159:0.309495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f: P:@0.681941:0.326108:0.703460:0.326108:0.703460:0.309639:0.681941:0.309639:0.000000:0.000000:0.000000:0.000000
0:@0.703543:0.329269:0.708496:0.329269:0.708496:0.319651:0.703543:0.319651:0.000000
 = (:@0.708495:0.325992:0.733347:0.325992:0.733347:0.309495:0.708495:0.309495:0.000000:0.000000:0.000000:0.000000
a, f (a):@0.733347:0.326108:0.777098:0.326108:0.777098:0.309639:0.733347:0.309639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
), al que lo man-:@0.777098:0.325992:0.891765:0.325992:0.891765:0.309495:0.777098:0.309495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tenemos fijo, y :@0.404239:0.343343:0.512086:0.343343:0.512086:0.326845:0.404239:0.326845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P =  a + h, f (a + h):@0.512278:0.343459:0.648811:0.343459:0.648811:0.326990:0.512278:0.326990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.540617:0.343343:0.546570:0.343343:0.546570:0.326845:0.540617:0.326845:0.000000
) que variará conforme | | se haga :@0.648811:0.343343:0.895925:0.343343:0.895925:0.326845:0.648811:0.326845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.820503:0.343459:0.829905:0.343459:0.829905:0.326990:0.820503:0.326990:0.000000
cada vez más pequeño. Determinemos la ecuación cartesiana de la :@0.404239:0.360694:0.895865:0.360694:0.895865:0.344196:0.404239:0.344196:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recta   que pasa por estos dos puntos. :@0.404239:0.378045:0.686054:0.378045:0.686054:0.361547:0.404239:0.361547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.444253:0.378160:0.452094:0.378160:0.452094:0.361692:0.444253:0.361692:0.000000
h:@0.451994:0.381389:0.457475:0.381389:0.457475:0.371788:0.451994:0.371788:0.000000
(:@0.432989:0.413859:0.438942:0.413859:0.438942:0.397362:0.432989:0.397362:0.000000
x, y:@0.438942:0.413975:0.461213:0.413975:0.461213:0.397506:0.438942:0.397506:0.000000:0.000000:0.000000:0.000000
)     tal que  –:@0.461213:0.413859:0.590380:0.413586:0.590380:0.397088:0.461213:0.397362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.471308:0.414409:0.485044:0.414409:0.485044:0.395569:0.471308:0.395569:0.000000
R:@0.489186:0.412891:0.503095:0.412891:0.503095:0.399444:0.489186:0.399444:0.000000
2:@0.503095:0.407501:0.508049:0.407501:0.508049:0.397883:0.503095:0.397883:0.000000
y f a:@0.569612:0.413702:0.619953:0.413702:0.619953:0.397233:0.569612:0.397233:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.603851:0.417256:0.626488:0.417256:0.626488:0.395766:0.603851:0.395766:0.000000:0.000000:0.000000
=:@0.629189:0.414222:0.639766:0.414222:0.639766:0.397941:0.629189:0.397941:0.000000
f a h:@0.647414:0.403479:0.695038:0.403479:0.695038:0.387010:0.647414:0.387010:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.672921:0.404000:0.683498:0.404000:0.683498:0.387719:0.672921:0.387719:0.000000
(:@0.655520:0.407041:0.661936:0.407041:0.661936:0.385550:0.655520:0.385550:0.000000
):@0.695149:0.407041:0.701564:0.407041:0.701564:0.385550:0.695149:0.385550:0.000000
–:@0.703422:0.403370:0.713922:0.403370:0.713922:0.386873:0.703422:0.386873:0.000000
f a:@0.719278:0.403486:0.743494:0.403486:0.743494:0.387017:0.719278:0.387017:0.000000:0.000000:0.000000
( ):@0.727400:0.407041:0.750037:0.407041:0.750037:0.385550:0.727400:0.385550:0.000000:0.000000:0.000000
h a h:@0.692533:0.425058:0.716159:0.427047:0.716159:0.410579:0.692533:0.408589:0.000000:0.000000:0.000000:0.000000:0.000000
x a ,  h ≠ 0.:@0.760328:0.413702:0.852302:0.413216:0.852302:0.396748:0.760328:0.397233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.770597:0.413586:0.781096:0.413586:0.781096:0.397088:0.770597:0.397088:0.000000
(:@0.752475:0.417256:0.758890:0.417256:0.758890:0.395766:0.752475:0.395766:0.000000
):@0.792412:0.417256:0.798827:0.417256:0.798827:0.395766:0.792412:0.395766:0.000000
Q h:@0.568043:0.462540:0.598328:0.462540:0.598328:0.446072:0.568043:0.446072:0.000000:0.000000:0.000000
( ):@0.581810:0.466095:0.604870:0.466095:0.604870:0.444604:0.581810:0.444604:0.000000:0.000000:0.000000
=:@0.607567:0.463061:0.618143:0.463061:0.618143:0.446780:0.607567:0.446780:0.000000
f a h:@0.625792:0.452318:0.673415:0.452318:0.673415:0.435849:0.625792:0.435849:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.651299:0.452838:0.661875:0.452838:0.661875:0.436558:0.651299:0.436558:0.000000
(:@0.633900:0.455879:0.640315:0.455879:0.640315:0.434389:0.633900:0.434389:0.000000
):@0.673528:0.455879:0.679944:0.455879:0.679944:0.434389:0.673528:0.434389:0.000000
–:@0.681802:0.452209:0.692301:0.452209:0.692301:0.435711:0.681802:0.435711:0.000000
f a:@0.697657:0.452325:0.721873:0.452325:0.721873:0.435856:0.697657:0.435856:0.000000:0.000000:0.000000
( ):@0.705778:0.455879:0.728414:0.455879:0.728414:0.434389:0.705778:0.434389:0.000000:0.000000:0.000000
h a h:@0.670913:0.473895:0.694538:0.475886:0.694538:0.459417:0.670913:0.457426:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.568460:0.511373:0.583256:0.511373:0.583256:0.494904:0.568460:0.494904:0.000000
=:@0.585587:0.511893:0.596163:0.511893:0.596163:0.495612:0.585587:0.495612:0.000000
lím:@0.598629:0.511257:0.620727:0.511257:0.620727:0.494759:0.598629:0.494759:0.000000:0.000000:0.000000
h:@0.599296:0.518146:0.604738:0.518146:0.604738:0.508614:0.599296:0.508614:0.000000
0:@0.615108:0.518079:0.620025:0.518079:0.620025:0.508530:0.615108:0.508530:0.000000
f a h:@0.626519:0.501163:0.674142:0.501163:0.674142:0.484695:0.626519:0.484695:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.652026:0.501684:0.662603:0.501684:0.662603:0.485403:0.652026:0.485403:0.000000
(:@0.634634:0.504717:0.641049:0.504717:0.641049:0.483226:0.634634:0.483226:0.000000
):@0.674262:0.504717:0.680678:0.504717:0.680678:0.483226:0.674262:0.483226:0.000000
–:@0.682534:0.501048:0.693033:0.501048:0.693033:0.484550:0.682534:0.484550:0.000000
f a:@0.698389:0.501163:0.722605:0.501163:0.722605:0.484695:0.698389:0.484695:0.000000:0.000000:0.000000
( ):@0.706511:0.504717:0.729148:0.504717:0.729148:0.483226:0.706511:0.483226:0.000000:0.000000:0.000000
h a h:@0.671645:0.522734:0.695264:0.524731:0.695264:0.508263:0.671645:0.506265:0.000000:0.000000:0.000000:0.000000:0.000000
df:@0.570598:0.548933:0.583699:0.548933:0.583699:0.532464:0.570598:0.532464:0.000000:0.000000
dx:@0.569982:0.569132:0.586261:0.569132:0.586261:0.552664:0.569982:0.552664:0.000000:0.000000
a:@0.596722:0.557768:0.605700:0.557768:0.605700:0.541299:0.596722:0.541299:0.000000
( ):@0.589612:0.561336:0.612248:0.561336:0.612248:0.539845:0.589612:0.539845:0.000000:0.000000:0.000000
,:@0.614321:0.557665:0.617076:0.557665:0.617076:0.541167:0.614321:0.541167:0.000000
m:@0.568470:0.604180:0.583266:0.604180:0.583266:0.587711:0.568470:0.587711:0.000000
=:@0.585597:0.604700:0.596173:0.604700:0.596173:0.588419:0.585597:0.588419:0.000000
df h > :@0.601298:0.595345:0.647939:0.594015:0.647939:0.577546:0.601298:0.578876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dx:@0.600681:0.615544:0.616961:0.615544:0.616961:0.599076:0.600681:0.599076:0.000000:0.000000
a:@0.627402:0.604180:0.636380:0.604180:0.636380:0.587711:0.627402:0.587711:0.000000
( ):@0.620288:0.607738:0.642925:0.607738:0.642925:0.586247:0.620288:0.586247:0.000000:0.000000:0.000000
m f '  a:@0.568462:0.642806:0.631536:0.642806:0.631536:0.626337:0.568462:0.626337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.585588:0.643326:0.596165:0.643326:0.596165:0.627046:0.585588:0.627046:0.000000
( ):@0.615420:0.646361:0.638057:0.646361:0.638057:0.624870:0.615420:0.624870:0.000000:0.000000:0.000000
.:@0.639396:0.642690:0.642151:0.642690:0.642151:0.626192:0.639396:0.626192:0.000000
Observamos que la pendiente de la recta es el cociente incremental :@0.404231:0.458863:0.895975:0.458863:0.895975:0.442366:0.404231:0.442366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.891777:0.458863:0.895919:0.458863:0.895919:0.442366:0.891777:0.442366:0.000000
Q  h:@0.404250:0.486639:0.435056:0.486639:0.435056:0.470170:0.404250:0.470170:0.000000:0.000000:0.000000:0.000000
( ) que se define como: :@0.419894:0.486523:0.588480:0.486523:0.588480:0.470026:0.419894:0.470026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y f a:@0.590734:0.437270:0.641074:0.437270:0.641074:0.420801:0.590734:0.420801:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.601002:0.437154:0.611502:0.437154:0.611502:0.420656:0.601002:0.420656:0.000000
( ):@0.624972:0.440825:0.647609:0.440825:0.647609:0.419334:0.624972:0.419334:0.000000:0.000000:0.000000
=:@0.650310:0.437790:0.660887:0.437790:0.660887:0.421510:0.650310:0.421510:0.000000
f:@0.668535:0.427047:0.672832:0.427047:0.672832:0.410579:0.668535:0.410579:0.000000
+:@0.694043:0.427568:0.704619:0.427568:0.704619:0.411287:0.694043:0.411287:0.000000
(:@0.676644:0.430609:0.683059:0.430609:0.683059:0.409118:0.676644:0.409118:0.000000
):@0.716272:0.430609:0.722688:0.430609:0.722688:0.409118:0.716272:0.409118:0.000000
–:@0.724545:0.426939:0.735045:0.426939:0.735045:0.410441:0.724545:0.410441:0.000000
f a:@0.740401:0.427054:0.764617:0.427054:0.764617:0.410585:0.740401:0.410585:0.000000:0.000000:0.000000
( ):@0.748521:0.430609:0.771158:0.430609:0.771158:0.409118:0.748521:0.409118:0.000000:0.000000:0.000000
h:@0.713656:0.448624:0.723058:0.448624:0.723058:0.432156:0.713656:0.432156:0.000000
x a:@0.781451:0.437274:0.813412:0.437274:0.813412:0.420805:0.781451:0.420805:0.000000:0.000000:0.000000
–:@0.791719:0.437159:0.802219:0.437159:0.802219:0.420661:0.791719:0.420661:0.000000
(:@0.773598:0.440825:0.780013:0.440825:0.780013:0.419334:0.773598:0.419334:0.000000
):@0.813535:0.440825:0.819950:0.440825:0.819950:0.419334:0.813535:0.419334:0.000000
Q h:@0.589164:0.486108:0.619449:0.486108:0.619449:0.469640:0.589164:0.469640:0.000000:0.000000:0.000000
( ):@0.602933:0.489662:0.625994:0.489662:0.625994:0.468171:0.602933:0.468171:0.000000:0.000000:0.000000
=:@0.628690:0.486629:0.639266:0.486629:0.639266:0.470348:0.628690:0.470348:0.000000
f:@0.646915:0.475886:0.651211:0.475886:0.651211:0.459417:0.646915:0.459417:0.000000
+:@0.672422:0.476406:0.682999:0.476406:0.682999:0.460126:0.672422:0.460126:0.000000
(:@0.655023:0.479446:0.661438:0.479446:0.661438:0.457956:0.655023:0.457956:0.000000
):@0.694652:0.479446:0.701067:0.479446:0.701067:0.457956:0.694652:0.457956:0.000000
–:@0.702923:0.475777:0.713423:0.475777:0.713423:0.459279:0.702923:0.459279:0.000000
f a:@0.718778:0.475893:0.742995:0.475893:0.742995:0.459424:0.718778:0.459424:0.000000:0.000000:0.000000
( ):@0.726901:0.479446:0.749537:0.479446:0.749537:0.457956:0.726901:0.457956:0.000000:0.000000:0.000000
h:@0.692034:0.497463:0.701435:0.497463:0.701435:0.480994:0.692034:0.480994:0.000000
m:@0.589583:0.534947:0.604379:0.534947:0.604379:0.518478:0.589583:0.518478:0.000000
=:@0.606710:0.535468:0.617286:0.535468:0.617286:0.519187:0.606710:0.519187:0.000000
lím:@0.619752:0.534831:0.641850:0.534831:0.641850:0.518334:0.619752:0.518334:0.000000:0.000000:0.000000
h:@0.620417:0.541714:0.625859:0.541714:0.625859:0.532182:0.620417:0.532182:0.000000
0:@0.636229:0.541647:0.641147:0.541647:0.641147:0.532098:0.636229:0.532098:0.000000
f:@0.647640:0.524731:0.651936:0.524731:0.651936:0.508263:0.647640:0.508263:0.000000
+:@0.673147:0.525252:0.683724:0.525252:0.683724:0.508971:0.673147:0.508971:0.000000
(:@0.655755:0.528285:0.662170:0.528285:0.662170:0.506794:0.655755:0.506794:0.000000
):@0.695384:0.528285:0.701799:0.528285:0.701799:0.506794:0.695384:0.506794:0.000000
–:@0.703657:0.524616:0.714156:0.524616:0.714156:0.508118:0.703657:0.508118:0.000000
f a:@0.719512:0.524731:0.743729:0.524731:0.743729:0.508263:0.719512:0.508263:0.000000:0.000000:0.000000
( ):@0.727633:0.528285:0.750270:0.528285:0.750270:0.506794:0.727633:0.506794:0.000000:0.000000:0.000000
h:@0.692768:0.546302:0.702169:0.546302:0.702169:0.529833:0.692768:0.529833:0.000000
df:@0.591721:0.572501:0.604822:0.572501:0.604822:0.556033:0.591721:0.556033:0.000000:0.000000
dx:@0.591105:0.592700:0.607384:0.592700:0.607384:0.576232:0.591105:0.576232:0.000000:0.000000
a:@0.617845:0.581336:0.626823:0.581336:0.626823:0.564867:0.617845:0.564867:0.000000
( ):@0.610733:0.584902:0.633370:0.584902:0.633370:0.563412:0.610733:0.563412:0.000000:0.000000:0.000000
,:@0.635443:0.581233:0.638198:0.581233:0.638198:0.564736:0.635443:0.564736:0.000000
m:@0.589591:0.627748:0.604387:0.627748:0.604387:0.611279:0.589591:0.611279:0.000000
=:@0.606718:0.628268:0.617295:0.628268:0.617295:0.611987:0.606718:0.611987:0.000000
df:@0.622419:0.618913:0.635520:0.618913:0.635520:0.602445:0.622419:0.602445:0.000000:0.000000
dx:@0.621803:0.639112:0.638082:0.639112:0.638082:0.622644:0.621803:0.622644:0.000000:0.000000
a:@0.648524:0.627748:0.657501:0.627748:0.657501:0.611279:0.648524:0.611279:0.000000
( ):@0.641412:0.631306:0.664048:0.631306:0.664048:0.609815:0.641412:0.609815:0.000000:0.000000:0.000000
m f '  a:@0.589583:0.666374:0.652657:0.666374:0.652657:0.649905:0.589583:0.649905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.606710:0.666894:0.617286:0.666894:0.617286:0.650614:0.606710:0.650614:0.000000
( ):@0.636542:0.669927:0.659178:0.669927:0.659178:0.648437:0.636542:0.648437:0.000000:0.000000:0.000000
.:@0.660519:0.666258:0.663274:0.666258:0.663274:0.649761:0.660519:0.649761:0.000000
,  :@0.751885:0.486526:0.762539:0.486526:0.762539:0.470028:0.751885:0.470028:0.000000:0.000000:0.000000
h ≠ :@0.762346:0.486641:0.790339:0.486641:0.790339:0.470173:0.762346:0.470173:0.000000:0.000000:0.000000:0.000000
0. :@0.790146:0.486526:0.805346:0.486526:0.805346:0.470028:0.790146:0.470028:0.000000:0.000000:0.000000
Luego, la ecuación cartesiana de la recta  se escribe como: :@0.404244:0.514186:0.825113:0.514186:0.825113:0.497689:0.404244:0.497688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.688038:0.514301:0.695879:0.514301:0.695879:0.497833:0.688038:0.497833:0.000000
h :@0.695773:0.517531:0.703669:0.517531:0.703669:0.507929:0.695773:0.507929:0.000000:0.000000
(:@0.404229:0.541846:0.410182:0.541846:0.410182:0.525349:0.404229:0.525349:0.000000
x, y:@0.410182:0.541962:0.432452:0.541962:0.432452:0.525493:0.410182:0.525493:0.000000:0.000000:0.000000:0.000000
) :@0.432452:0.541846:0.442547:0.541846:0.442547:0.525349:0.432452:0.525349:0.000000:0.000000
∈ :@0.442547:0.542396:0.461100:0.542396:0.461100:0.523556:0.442547:0.523556:0.000000:0.000000
R:@0.461100:0.540878:0.475009:0.540878:0.475009:0.527431:0.461100:0.527431:0.000000
2:@0.475015:0.535494:0.479968:0.535494:0.479968:0.525876:0.475015:0.525876:0.000000
 tal que :@0.479969:0.541847:0.537398:0.541847:0.537398:0.525349:0.479969:0.525349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y – f (a)  Q  h x – a:@0.537398:0.541963:0.688843:0.541963:0.688843:0.525494:0.537398:0.525494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=  ( )(:@0.595830:0.541847:0.654069:0.541847:0.654069:0.525349:0.595830:0.525349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
), con :@0.688843:0.541847:0.732787:0.541847:0.732787:0.525349:0.688843:0.525349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h ≠ :@0.732787:0.541963:0.761357:0.541963:0.761357:0.525494:0.732787:0.525494:0.000000:0.000000:0.000000:0.000000
0.:@0.761357:0.541847:0.772608:0.541847:0.772608:0.525349:0.761357:0.525349:0.000000:0.000000
En la figura 4.21. se muestran las posiciones de los puntos  ,  ,  , ..., :@0.404237:0.576549:0.895914:0.576549:0.895914:0.560051:0.404237:0.560051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P P P:@0.812398:0.576664:0.866755:0.576664:0.866755:0.560195:0.812398:0.560195:0.000000:0.000000:0.000000:0.000000:0.000000
2 :@0.821163:0.579825:0.828531:0.579825:0.828531:0.570207:0.821163:0.570207:0.000000:0.000000
3 :@0.843955:0.579825:0.851323:0.579825:0.851323:0.570207:0.843955:0.570207:0.000000:0.000000
4 :@0.866745:0.579825:0.874113:0.579825:0.874113:0.570207:0.866745:0.570207:0.000000:0.000000
que corresponden a valores de :@0.404235:0.593899:0.621603:0.593899:0.621603:0.577402:0.404235:0.577402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 cada vez más pequeños. También :@0.646821:0.593899:0.895996:0.593899:0.895996:0.577402:0.646821:0.577402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se muestran las posiciones de las rectas :@0.404235:0.614142:0.681593:0.614142:0.681593:0.597644:0.404235:0.597644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L L L:@0.683254:0.614402:0.734600:0.614392:0.734600:0.597923:0.683254:0.597933:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.691002:0.616562:0.696444:0.616562:0.696444:0.607030:0.691002:0.607030:0.000000
1:@0.692574:0.605256:0.697492:0.605256:0.697492:0.595707:0.692574:0.595707:0.000000
( ):@0.689169:0.607410:0.700365:0.607410:0.700365:0.594971:0.689169:0.594971:0.000000:0.000000:0.000000
, ,:@0.703305:0.614276:0.725796:0.614276:0.725796:0.597779:0.703305:0.597779:0.000000:0.000000:0.000000
h:@0.714769:0.616562:0.720210:0.616562:0.720210:0.607030:0.714769:0.607030:0.000000
2:@0.712940:0.606244:0.717857:0.606244:0.717857:0.596695:0.712940:0.596695:0.000000
h:@0.734506:0.616562:0.739948:0.616562:0.739948:0.607030:0.734506:0.607030:0.000000
3:@0.736547:0.605256:0.741464:0.605256:0.741464:0.595707:0.736547:0.595707:0.000000
( ):@0.732674:0.607410:0.745285:0.607410:0.745285:0.594971:0.732674:0.594971:0.000000:0.000000:0.000000
,:@0.748222:0.614276:0.750976:0.614276:0.750976:0.597779:0.748222:0.597779:0.000000
…:@0.750726:0.614913:0.769991:0.614913:0.769991:0.598632:0.750726:0.598632:0.000000
 :@0.770935:0.614247:0.775077:0.614247:0.775077:0.597779:0.770935:0.597779:0.000000
que pasan por :@0.774210:0.614132:0.878934:0.614132:0.878934:0.597634:0.774210:0.597634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.878068:0.614247:0.886852:0.614247:0.886852:0.597779:0.878068:0.597779:0.000000
0 :@0.886817:0.617413:0.894185:0.617413:0.894185:0.607795:0.886817:0.607795:0.000000:0.000000
 :@0.891770:0.617413:0.894185:0.617413:0.894185:0.607795:0.891770:0.607795:0.000000
y por cada uno de los puntos  ,  ,  , ..., respectivamente, y la recta :@0.404236:0.631486:0.895906:0.631486:0.895906:0.614989:0.404236:0.614989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P P P:@0.617732:0.631602:0.673054:0.631602:0.673054:0.615133:0.617732:0.615133:0.000000:0.000000:0.000000:0.000000:0.000000
2 :@0.626525:0.634764:0.633893:0.634764:0.633893:0.625146:0.626525:0.625146:0.000000:0.000000
3 :@0.649791:0.634764:0.657159:0.634764:0.657159:0.625146:0.649791:0.625146:0.000000:0.000000
4 :@0.673057:0.634764:0.680425:0.634764:0.680425:0.625146:0.673057:0.625146:0.000000:0.000000
tangente   a la gráfica de la función :@0.404240:0.648837:0.659464:0.648837:0.659464:0.632339:0.404240:0.632339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.471782:0.648953:0.479623:0.648953:0.479623:0.632484:0.471782:0.632484:0.000000
f.:@0.659464:0.648953:0.666033:0.648953:0.666033:0.632484:0.659464:0.632484:0.000000:0.000000
Desde el punto de vista intuitivo, podemos observar que para  > 0 :@0.404240:0.683539:0.895908:0.683539:0.895908:0.667041:0.404240:0.667041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h   :@0.853307:0.683654:0.882577:0.683654:0.882577:0.667186:0.853307:0.667186:0.000000:0.000000:0.000000:0.000000
cada vez más pequeño, la recta  se acerca cada vez más a la recta   :@0.404240:0.700889:0.895908:0.700889:0.895908:0.684392:0.404240:0.684392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.629158:0.701005:0.636999:0.701005:0.636999:0.684536:0.629158:0.684536:0.000000
h  :@0.636920:0.704235:0.647220:0.704235:0.647220:0.694634:0.636920:0.694634:0.000000:0.000000:0.000000
L,:@0.880856:0.701005:0.891741:0.701005:0.891741:0.684536:0.880856:0.684536:0.000000:0.000000
lo que implica que el cociente incremental :@0.404240:0.718240:0.705621:0.718240:0.705621:0.701742:0.404240:0.701742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q (h) :@0.704851:0.718356:0.744518:0.718356:0.744518:0.701887:0.704851:0.701887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se aproxima cada vez :@0.743747:0.718240:0.895999:0.718240:0.895999:0.701742:0.743747:0.701742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
más a la pendiente   de la recta tangente   que tiene como ecuación :@0.404240:0.735591:0.895864:0.735591:0.895864:0.719093:0.404240:0.719093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.539539:0.735707:0.554335:0.735707:0.554335:0.719238:0.539539:0.719238:0.000000
L:@0.700942:0.735707:0.708783:0.735707:0.708783:0.719238:0.700942:0.719238:0.000000
cartesiana (:@0.404240:0.752942:0.485269:0.752942:0.485269:0.736444:0.404240:0.736444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x, y Q h h:@0.485269:0.753057:0.512175:0.750619:0.512175:0.734150:0.485269:0.736589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)  –:@0.507540:0.752942:0.531059:0.750510:0.531059:0.734012:0.507540:0.736444:0.000000:0.000000:0.000000:0.000000
∈ :@0.517635:0.753491:0.536187:0.753491:0.536187:0.734651:0.517635:0.734651:0.000000:0.000000
R:@0.536187:0.751973:0.550097:0.751973:0.550097:0.738526:0.536187:0.738526:0.000000
2:@0.550091:0.746590:0.555044:0.746590:0.555044:0.736972:0.550091:0.736972:0.000000
 tal que :@0.555045:0.752942:0.612474:0.752942:0.612474:0.736444:0.555045:0.736444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y – f  a f a:@0.612474:0.753057:0.677582:0.755251:0.677582:0.738783:0.612474:0.736589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) = :@0.646921:0.752942:0.686896:0.752942:0.686896:0.736444:0.646921:0.736444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m (x –a).:@0.686896:0.753057:0.750182:0.753057:0.750182:0.736589:0.686896:0.736589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se escribirá :@0.404236:0.801726:0.487404:0.801726:0.487404:0.785228:0.404236:0.785228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y f a h:@0.489868:0.704055:0.533796:0.701781:0.533796:0.685313:0.489868:0.687586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.500136:0.703940:0.510636:0.703940:0.510636:0.687442:0.500136:0.687442:0.000000
( ) ):@0.524105:0.707609:0.540324:0.705342:0.540324:0.683851:0.524105:0.686118:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.549443:0.704576:0.560019:0.704576:0.560019:0.688295:0.549443:0.688295:0.000000
f a h:@0.567668:0.693833:0.615291:0.693833:0.615291:0.677364:0.567668:0.677364:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.593175:0.694353:0.603751:0.694353:0.603751:0.678072:0.593175:0.678072:0.000000
(:@0.575776:0.697393:0.582191:0.697393:0.582191:0.675903:0.575776:0.675903:0.000000
):@0.615404:0.697393:0.621820:0.697393:0.621820:0.675903:0.615404:0.675903:0.000000
–:@0.623678:0.693724:0.634177:0.693724:0.634177:0.677226:0.623678:0.677226:0.000000
f a:@0.639533:0.693840:0.663749:0.693840:0.663749:0.677371:0.639533:0.677371:0.000000:0.000000:0.000000
( ):@0.647654:0.697393:0.670290:0.697393:0.670290:0.675903:0.647654:0.675903:0.000000:0.000000:0.000000
h:@0.612788:0.715410:0.622190:0.715410:0.622190:0.698941:0.612788:0.698941:0.000000
x a:@0.680583:0.704060:0.712544:0.704060:0.712544:0.687591:0.680583:0.687591:0.000000:0.000000:0.000000
–:@0.690851:0.703944:0.701351:0.703944:0.701351:0.687446:0.690851:0.687446:0.000000
( ( ):@0.672730:0.707609:0.683391:0.709967:0.683391:0.688477:0.672730:0.686118:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.712667:0.707609:0.719082:0.707609:0.719082:0.686118:0.712667:0.686118:0.000000
( ) ):@0.502065:0.756447:0.518704:0.754180:0.518704:0.732690:0.502065:0.734957:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.527822:0.753414:0.538399:0.753414:0.538399:0.737134:0.527822:0.737134:0.000000
f a h:@0.546047:0.742671:0.593671:0.742671:0.593671:0.726203:0.546047:0.726203:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.571554:0.743192:0.582131:0.743192:0.582131:0.726911:0.571554:0.726911:0.000000
(:@0.554155:0.746232:0.560570:0.746232:0.560570:0.724741:0.554155:0.724741:0.000000
):@0.593784:0.746232:0.600199:0.746232:0.600199:0.724741:0.593784:0.724741:0.000000
–:@0.602055:0.742563:0.612555:0.742563:0.612555:0.726065:0.602055:0.726065:0.000000
f a:@0.617910:0.742678:0.642127:0.742678:0.642127:0.726210:0.617910:0.726210:0.000000:0.000000:0.000000
( ):@0.626033:0.746232:0.648670:0.746232:0.648670:0.724741:0.626033:0.724741:0.000000:0.000000:0.000000
h:@0.591166:0.764249:0.600568:0.764249:0.600568:0.747780:0.591166:0.747780:0.000000
m h:@0.488715:0.801731:0.512901:0.799464:0.512901:0.782996:0.488715:0.785262:0.000000:0.000000:0.000000
=:@0.505842:0.802252:0.516419:0.802252:0.516419:0.785971:0.505842:0.785971:0.000000
lím:@0.518885:0.801616:0.540982:0.801616:0.540982:0.785118:0.518885:0.785118:0.000000:0.000000:0.000000
h:@0.519550:0.808499:0.524991:0.808499:0.524991:0.798967:0.519550:0.798967:0.000000
0:@0.535361:0.808432:0.540278:0.808432:0.540278:0.798884:0.535361:0.798884:0.000000
f a h:@0.546772:0.791516:0.594396:0.791516:0.594396:0.775047:0.546772:0.775047:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.572279:0.792036:0.582856:0.792036:0.582856:0.775755:0.572279:0.775755:0.000000
(:@0.554887:0.795070:0.561302:0.795070:0.561302:0.773580:0.554887:0.773580:0.000000
):@0.594516:0.795070:0.600931:0.795070:0.600931:0.773580:0.594516:0.773580:0.000000
–:@0.602789:0.791400:0.613289:0.791400:0.613289:0.774902:0.602789:0.774902:0.000000
f a:@0.618644:0.791516:0.642861:0.791516:0.642861:0.775047:0.618644:0.775047:0.000000:0.000000:0.000000
( ):@0.626765:0.795070:0.649402:0.795070:0.649402:0.773580:0.626765:0.773580:0.000000:0.000000:0.000000
h:@0.591900:0.813087:0.601301:0.813087:0.601301:0.796618:0.591900:0.796618:0.000000
df:@0.490861:0.839293:0.503962:0.839293:0.503962:0.822824:0.490861:0.822824:0.000000:0.000000
dx m:@0.490245:0.859492:0.538240:0.858268:0.538240:0.841799:0.490245:0.843023:0.000000:0.000000:0.000000:0.000000
a:@0.516985:0.848127:0.525962:0.848127:0.525962:0.831659:0.516985:0.831659:0.000000
( ):@0.509865:0.851688:0.532502:0.851688:0.532502:0.830197:0.509865:0.830197:0.000000:0.000000:0.000000
,:@0.534575:0.848019:0.537330:0.848019:0.537330:0.831521:0.534575:0.831521:0.000000
m:@0.488724:0.894533:0.503519:0.894533:0.503519:0.878064:0.488724:0.878064:0.000000
=:@0.505850:0.895054:0.516427:0.895054:0.516427:0.878773:0.505850:0.878773:0.000000
df:@0.521552:0.885699:0.534652:0.885699:0.534652:0.869230:0.521552:0.869230:0.000000:0.000000
dx:@0.520935:0.905898:0.537214:0.905898:0.537214:0.889429:0.520935:0.889429:0.000000:0.000000
a f '  a:@0.547656:0.894533:0.586511:0.896894:0.586511:0.880425:0.547656:0.878064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) ( ):@0.540544:0.898090:0.593032:0.900449:0.593032:0.878958:0.540544:0.876599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m f '  a:@0.488715:0.933159:0.551790:0.933159:0.551790:0.916690:0.488715:0.916690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.505842:0.933680:0.516419:0.933680:0.516419:0.917399:0.505842:0.917399:0.000000
( ):@0.535674:0.936713:0.558310:0.936713:0.558310:0.915222:0.535674:0.915222:0.000000:0.000000:0.000000
.:@0.559652:0.933043:0.562406:0.933043:0.562406:0.916546:0.559652:0.916546:0.000000
 siempre que el límite exista y se le :@0.654060:0.801725:0.895894:0.801725:0.895894:0.785227:0.654060:0.785227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llamará derivada de   con respecto de   en el punto  =   que se nota: :@0.404228:0.829385:0.895916:0.829385:0.895916:0.812887:0.404228:0.812887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.545249:0.829501:0.549546:0.829501:0.549546:0.813032:0.545249:0.813032:0.000000
x:@0.670318:0.829501:0.677793:0.829501:0.677793:0.813032:0.670318:0.813032:0.000000
x  a,:@0.765871:0.829501:0.802961:0.829501:0.802961:0.813032:0.765871:0.813032:0.000000:0.000000:0.000000:0.000000:0.000000
y f a:@0.408372:0.712004:0.458712:0.712004:0.458712:0.695535:0.408372:0.695535:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.418641:0.711888:0.429140:0.711888:0.429140:0.695391:0.418641:0.695391:0.000000
( ):@0.442609:0.715557:0.465246:0.715557:0.465246:0.694067:0.442609:0.694067:0.000000:0.000000:0.000000
=:@0.467947:0.712524:0.478524:0.712524:0.478524:0.696244:0.467947:0.696244:0.000000
f a:@0.486172:0.701781:0.510389:0.701781:0.510389:0.685313:0.486172:0.685313:0.000000:0.000000:0.000000
+:@0.511679:0.702302:0.522256:0.702302:0.522256:0.686021:0.511679:0.686021:0.000000
(:@0.494280:0.705342:0.500696:0.705342:0.500696:0.683851:0.494280:0.683851:0.000000
–:@0.542182:0.701673:0.552682:0.701673:0.552682:0.685175:0.542182:0.685175:0.000000
f a:@0.558037:0.701788:0.582254:0.701788:0.582254:0.685320:0.558037:0.685320:0.000000:0.000000:0.000000
( ):@0.566158:0.705342:0.588795:0.705342:0.588795:0.683851:0.566158:0.683851:0.000000:0.000000:0.000000
h:@0.531293:0.723359:0.540695:0.723359:0.540695:0.706890:0.531293:0.706890:0.000000
x a:@0.599087:0.712008:0.631049:0.712008:0.631049:0.695540:0.599087:0.695540:0.000000:0.000000:0.000000
–:@0.609356:0.711893:0.619855:0.711893:0.619855:0.695395:0.609356:0.695395:0.000000
(:@0.591235:0.715557:0.597650:0.715557:0.597650:0.694067:0.591235:0.694067:0.000000
):@0.631172:0.715557:0.637587:0.715557:0.637587:0.694067:0.631172:0.694067:0.000000
Q h:@0.406801:0.760841:0.437086:0.760841:0.437086:0.744372:0.406801:0.744372:0.000000:0.000000:0.000000
( ):@0.420570:0.764396:0.443630:0.764396:0.443630:0.742905:0.420570:0.742905:0.000000:0.000000:0.000000
=:@0.446327:0.761362:0.456903:0.761362:0.456903:0.745081:0.446327:0.745081:0.000000
f a:@0.464552:0.750619:0.488768:0.750619:0.488768:0.734150:0.464552:0.734150:0.000000:0.000000:0.000000
+:@0.490059:0.751139:0.500635:0.751139:0.500635:0.734858:0.490059:0.734858:0.000000
(:@0.472660:0.754180:0.479075:0.754180:0.479075:0.732690:0.472660:0.732690:0.000000
f a:@0.536415:0.750626:0.560632:0.750626:0.560632:0.734157:0.536415:0.734157:0.000000:0.000000:0.000000
( ):@0.544538:0.754180:0.567174:0.754180:0.567174:0.732690:0.544538:0.732690:0.000000:0.000000:0.000000
h:@0.509671:0.772197:0.519072:0.772197:0.519072:0.755728:0.509671:0.755728:0.000000
m:@0.407218:0.809675:0.422014:0.809675:0.422014:0.793206:0.407218:0.793206:0.000000
=:@0.424345:0.810195:0.434922:0.810195:0.434922:0.793915:0.424345:0.793915:0.000000
lím:@0.437387:0.809559:0.459485:0.809559:0.459485:0.793061:0.437387:0.793061:0.000000:0.000000:0.000000
h:@0.438054:0.816447:0.443496:0.816447:0.443496:0.806915:0.438054:0.806915:0.000000
0:@0.453866:0.816380:0.458783:0.816380:0.458783:0.806831:0.453866:0.806831:0.000000
f a:@0.465277:0.799464:0.489493:0.799464:0.489493:0.782996:0.465277:0.782996:0.000000:0.000000:0.000000
+:@0.490784:0.799985:0.501361:0.799985:0.501361:0.783704:0.490784:0.783704:0.000000
(:@0.473392:0.803019:0.479807:0.803019:0.479807:0.781528:0.473392:0.781528:0.000000
):@0.513020:0.803019:0.519436:0.803019:0.519436:0.781528:0.513020:0.781528:0.000000
–:@0.521294:0.799349:0.531793:0.799349:0.531793:0.782851:0.521294:0.782851:0.000000
f a:@0.537149:0.799464:0.561365:0.799464:0.561365:0.782996:0.537149:0.782996:0.000000:0.000000:0.000000
( ):@0.545270:0.803019:0.567906:0.803019:0.567906:0.781528:0.545270:0.781528:0.000000:0.000000:0.000000
h dx:@0.510404:0.821035:0.541237:0.823220:0.541237:0.806752:0.510404:0.804566:0.000000:0.000000:0.000000:0.000000
df:@0.409366:0.847242:0.422466:0.847242:0.422466:0.830773:0.409366:0.830773:0.000000:0.000000
dx:@0.408749:0.867441:0.425028:0.867441:0.425028:0.850972:0.408749:0.850972:0.000000:0.000000
a:@0.435489:0.856082:0.444467:0.856082:0.444467:0.839613:0.435489:0.839613:0.000000
( ):@0.428370:0.859637:0.451006:0.859637:0.451006:0.838146:0.428370:0.838146:0.000000:0.000000:0.000000
,  esto es, :@0.453079:0.855966:0.520452:0.857046:0.520452:0.840548:0.453079:0.839468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.407228:0.902481:0.422024:0.902481:0.422024:0.886012:0.407228:0.886012:0.000000
=:@0.424355:0.903002:0.434932:0.903002:0.434932:0.886721:0.424355:0.886721:0.000000
df:@0.440056:0.893647:0.453157:0.893647:0.453157:0.877178:0.440056:0.877178:0.000000:0.000000
dx:@0.439440:0.913846:0.455719:0.913846:0.455719:0.897377:0.439440:0.897377:0.000000:0.000000
a:@0.466161:0.902481:0.475138:0.902481:0.475138:0.886012:0.466161:0.886012:0.000000
( ):@0.459048:0.906039:0.481685:0.906039:0.481685:0.884548:0.459048:0.884548:0.000000:0.000000:0.000000
m f '  a:@0.407220:0.941107:0.470294:0.941107:0.470294:0.924639:0.407220:0.924639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.424347:0.941628:0.434923:0.941628:0.434923:0.925347:0.424347:0.925347:0.000000
( ):@0.454178:0.944662:0.476815:0.944662:0.476815:0.923171:0.454178:0.923171:0.000000:0.000000:0.000000
.:@0.478156:0.940992:0.480911:0.940992:0.480911:0.924494:0.478156:0.924494:0.000000
y f a:@0.524589:0.667790:0.574929:0.667790:0.574929:0.651321:0.524589:0.651321:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.534857:0.667674:0.545357:0.667674:0.545357:0.651176:0.534857:0.651176:0.000000
( ) (:@0.558826:0.671344:0.597650:0.673556:0.597650:0.652065:0.558826:0.649854:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.584164:0.668310:0.594740:0.668310:0.594740:0.652029:0.584164:0.652029:0.000000
f a h:@0.602389:0.657567:0.650012:0.657567:0.650012:0.641098:0.602389:0.641098:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.627896:0.658088:0.638472:0.658088:0.638472:0.641807:0.627896:0.641807:0.000000
(:@0.610497:0.661129:0.616912:0.661129:0.616912:0.639638:0.610497:0.639638:0.000000
):@0.650125:0.661129:0.656541:0.661129:0.656541:0.639638:0.650125:0.639638:0.000000
–:@0.658399:0.657458:0.668898:0.657458:0.668898:0.640961:0.658399:0.640961:0.000000
f a:@0.674254:0.657574:0.698470:0.657574:0.698470:0.641105:0.674254:0.641105:0.000000:0.000000:0.000000
( ):@0.682375:0.661129:0.705011:0.661129:0.705011:0.639638:0.682375:0.639638:0.000000:0.000000:0.000000
h:@0.647509:0.679146:0.656911:0.679146:0.656911:0.662677:0.647509:0.662677:0.000000
x a:@0.715304:0.667795:0.747265:0.667795:0.747265:0.651327:0.715304:0.651327:0.000000:0.000000:0.000000
–:@0.725572:0.667680:0.736072:0.667680:0.736072:0.651182:0.725572:0.651182:0.000000
(:@0.707451:0.671344:0.713867:0.671344:0.713867:0.649854:0.707451:0.649854:0.000000
):@0.747388:0.671344:0.753803:0.671344:0.753803:0.649854:0.747388:0.649854:0.000000
Q h:@0.523017:0.716628:0.553302:0.716628:0.553302:0.700159:0.523017:0.700159:0.000000:0.000000:0.000000
( ):@0.536786:0.720183:0.559847:0.720183:0.559847:0.698692:0.536786:0.698692:0.000000:0.000000:0.000000
=:@0.562543:0.717149:0.573120:0.717149:0.573120:0.700868:0.562543:0.700868:0.000000
f a h:@0.580768:0.706406:0.628392:0.706406:0.628392:0.689937:0.580768:0.689937:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.606275:0.706926:0.616852:0.706926:0.616852:0.690645:0.606275:0.690645:0.000000
(:@0.588876:0.709967:0.595291:0.709967:0.595291:0.688477:0.588876:0.688477:0.000000
):@0.628505:0.709967:0.634920:0.709967:0.634920:0.688477:0.628505:0.688477:0.000000
–:@0.636776:0.706297:0.647276:0.706297:0.647276:0.689799:0.636776:0.689799:0.000000
f a:@0.652632:0.706413:0.676848:0.706413:0.676848:0.689944:0.652632:0.689944:0.000000:0.000000:0.000000
h:@0.625887:0.727983:0.635289:0.727983:0.635289:0.711514:0.625887:0.711514:0.000000
m:@0.523435:0.765461:0.538230:0.765461:0.538230:0.748992:0.523435:0.748992:0.000000
=:@0.540561:0.765981:0.551138:0.765981:0.551138:0.749700:0.540561:0.749700:0.000000
lím:@0.553604:0.765345:0.575701:0.765345:0.575701:0.748847:0.553604:0.748847:0.000000:0.000000:0.000000
h:@0.554271:0.772234:0.559712:0.772234:0.559712:0.762702:0.554271:0.762702:0.000000
0:@0.570082:0.772167:0.575000:0.772167:0.575000:0.762618:0.570082:0.762618:0.000000
f a h:@0.581493:0.755251:0.629117:0.755251:0.629117:0.738783:0.581493:0.738783:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.607000:0.755772:0.617577:0.755772:0.617577:0.739491:0.607000:0.739491:0.000000
(:@0.589608:0.758805:0.596023:0.758805:0.596023:0.737314:0.589608:0.737314:0.000000
):@0.629237:0.758805:0.635652:0.758805:0.635652:0.737314:0.629237:0.737314:0.000000
–:@0.637510:0.755136:0.648010:0.755136:0.648010:0.738638:0.637510:0.738638:0.000000
( ):@0.661486:0.758805:0.684123:0.758805:0.684123:0.737314:0.661486:0.737314:0.000000:0.000000:0.000000
h:@0.626621:0.776822:0.636022:0.776822:0.636022:0.760353:0.626621:0.760353:0.000000
df:@0.525575:0.803021:0.538675:0.803021:0.538675:0.786552:0.525575:0.786552:0.000000:0.000000
a:@0.551698:0.811856:0.560676:0.811856:0.560676:0.795387:0.551698:0.795387:0.000000
( ):@0.544586:0.815424:0.567223:0.815424:0.567223:0.793933:0.544586:0.793933:0.000000:0.000000:0.000000
,:@0.569296:0.811753:0.572051:0.811753:0.572051:0.795255:0.569296:0.795255:0.000000
=:@0.540571:0.858789:0.551148:0.858789:0.551148:0.842508:0.540571:0.842508:0.000000
df:@0.556273:0.849434:0.569373:0.849434:0.569373:0.832965:0.556273:0.832965:0.000000:0.000000
dx:@0.555656:0.869633:0.571935:0.869633:0.571935:0.853164:0.555656:0.853164:0.000000:0.000000
a:@0.582385:0.858271:0.591362:0.858271:0.591362:0.841802:0.582385:0.841802:0.000000
( ):@0.575265:0.861826:0.597901:0.861826:0.597901:0.840335:0.575265:0.840335:0.000000:0.000000:0.000000
m:@0.523436:0.896894:0.538232:0.896894:0.538232:0.880425:0.523436:0.880425:0.000000
=:@0.540563:0.897414:0.551140:0.897414:0.551140:0.881134:0.540563:0.881134:0.000000
.:@0.594373:0.896778:0.597127:0.896778:0.597127:0.880280:0.594373:0.880280:0.000000
. :@0.601154:0.857046:0.608051:0.857046:0.608051:0.840548:0.601154:0.840548:0.000000:0.000000
En muchos libros se nota también::@0.404244:0.884706:0.649625:0.884706:0.649625:0.868208:0.404244:0.868208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y f a:@0.408372:0.670002:0.458712:0.670002:0.458712:0.653534:0.408372:0.653534:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.418641:0.669887:0.429140:0.669887:0.429140:0.653389:0.418641:0.653389:0.000000
( ):@0.442609:0.673556:0.465246:0.673556:0.465246:0.652065:0.442609:0.652065:0.000000:0.000000:0.000000
=:@0.467947:0.670523:0.478524:0.670523:0.478524:0.654242:0.467947:0.654242:0.000000
f a h:@0.486172:0.659780:0.533796:0.659780:0.533796:0.643311:0.486172:0.643311:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.511679:0.660301:0.522256:0.660301:0.522256:0.644020:0.511679:0.644020:0.000000
(:@0.494280:0.663340:0.500696:0.663340:0.500696:0.641850:0.494280:0.641850:0.000000
):@0.533909:0.663340:0.540324:0.663340:0.540324:0.641850:0.533909:0.641850:0.000000
–:@0.542182:0.659671:0.552682:0.659671:0.552682:0.643174:0.542182:0.643174:0.000000
f a:@0.558037:0.659787:0.582254:0.659787:0.582254:0.643318:0.558037:0.643318:0.000000:0.000000:0.000000
( ):@0.566158:0.663340:0.588795:0.663340:0.588795:0.641850:0.566158:0.641850:0.000000:0.000000:0.000000
h:@0.531293:0.681357:0.540695:0.681357:0.540695:0.664888:0.531293:0.664888:0.000000
x a:@0.599087:0.670007:0.631049:0.670007:0.631049:0.653538:0.599087:0.653538:0.000000:0.000000:0.000000
–:@0.609356:0.669891:0.619855:0.669891:0.619855:0.653394:0.609356:0.653394:0.000000
):@0.631172:0.673556:0.637587:0.673556:0.637587:0.652065:0.631172:0.652065:0.000000
Q h:@0.406801:0.718840:0.437086:0.718840:0.437086:0.702371:0.406801:0.702371:0.000000:0.000000:0.000000
( ):@0.420570:0.722395:0.443630:0.722395:0.443630:0.700904:0.420570:0.700904:0.000000:0.000000:0.000000
=:@0.446327:0.719360:0.456903:0.719360:0.456903:0.703080:0.446327:0.703080:0.000000
f a h:@0.464552:0.708617:0.512175:0.708617:0.512175:0.692149:0.464552:0.692149:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.490059:0.709138:0.500635:0.709138:0.500635:0.692857:0.490059:0.692857:0.000000
(:@0.472660:0.712179:0.479075:0.712179:0.479075:0.690688:0.472660:0.690688:0.000000
):@0.512288:0.712179:0.518704:0.712179:0.518704:0.690688:0.512288:0.690688:0.000000
–:@0.520560:0.708509:0.531059:0.708509:0.531059:0.692011:0.520560:0.692011:0.000000
f a:@0.536415:0.708624:0.560632:0.708624:0.560632:0.692156:0.536415:0.692156:0.000000:0.000000:0.000000
( ):@0.544538:0.712179:0.567174:0.712179:0.567174:0.690688:0.544538:0.690688:0.000000:0.000000:0.000000
h:@0.509671:0.730196:0.519072:0.730196:0.519072:0.713727:0.509671:0.713727:0.000000
m:@0.407218:0.767673:0.422014:0.767673:0.422014:0.751205:0.407218:0.751205:0.000000
=:@0.424345:0.768194:0.434922:0.768194:0.434922:0.751913:0.424345:0.751913:0.000000
lím:@0.437387:0.767558:0.459485:0.767558:0.459485:0.751060:0.437387:0.751060:0.000000:0.000000:0.000000
h:@0.438054:0.774445:0.443496:0.774445:0.443496:0.764913:0.438054:0.764913:0.000000
0:@0.453866:0.774378:0.458783:0.774378:0.458783:0.764830:0.453866:0.764830:0.000000
f a h:@0.465277:0.757463:0.512901:0.757463:0.512901:0.740994:0.465277:0.740994:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.490784:0.757983:0.501361:0.757983:0.501361:0.741703:0.490784:0.741703:0.000000
(:@0.473392:0.761018:0.479807:0.761018:0.479807:0.739527:0.473392:0.739527:0.000000
):@0.513020:0.761018:0.519436:0.761018:0.519436:0.739527:0.513020:0.739527:0.000000
–:@0.521294:0.757347:0.531793:0.757347:0.531793:0.740850:0.521294:0.740850:0.000000
f a:@0.537149:0.757463:0.561365:0.757463:0.561365:0.740994:0.537149:0.740994:0.000000:0.000000:0.000000
( ):@0.545270:0.761018:0.567906:0.761018:0.567906:0.739527:0.545270:0.739527:0.000000:0.000000:0.000000
h:@0.510404:0.779033:0.519806:0.779033:0.519806:0.762564:0.510404:0.762564:0.000000
df:@0.409358:0.805233:0.422459:0.805233:0.422459:0.788764:0.409358:0.788764:0.000000:0.000000
dx:@0.408742:0.825432:0.425021:0.825432:0.425021:0.808963:0.408742:0.808963:0.000000:0.000000
a:@0.435482:0.814067:0.444460:0.814067:0.444460:0.797598:0.435482:0.797598:0.000000
( ):@0.428370:0.817635:0.451006:0.817635:0.451006:0.796144:0.428370:0.796144:0.000000:0.000000:0.000000
,:@0.453079:0.813965:0.455834:0.813965:0.455834:0.797467:0.453079:0.797467:0.000000
m:@0.407228:0.860479:0.422024:0.860479:0.422024:0.844010:0.407228:0.844010:0.000000
=:@0.424355:0.861000:0.434932:0.861000:0.434932:0.844719:0.424355:0.844719:0.000000
df:@0.440056:0.851645:0.453157:0.851645:0.453157:0.835176:0.440056:0.835176:0.000000:0.000000
dx:@0.439440:0.871844:0.455719:0.871844:0.455719:0.855375:0.439440:0.855375:0.000000:0.000000
a:@0.466161:0.860479:0.475138:0.860479:0.475138:0.844010:0.466161:0.844010:0.000000
( ):@0.459048:0.864037:0.481685:0.864037:0.481685:0.842546:0.459048:0.842546:0.000000:0.000000:0.000000
m f '  a:@0.407220:0.899105:0.470294:0.899105:0.470294:0.882637:0.407220:0.882637:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.424347:0.899626:0.434923:0.899626:0.434923:0.883345:0.424347:0.883345:0.000000
( ):@0.454178:0.902660:0.476815:0.902660:0.476815:0.881169:0.454178:0.881169:0.000000:0.000000:0.000000
.:@0.478156:0.898990:0.480911:0.898990:0.480911:0.882492:0.478156:0.882492:0.000000
Desequilibrio cognitivo:@0.199646:0.238907:0.363493:0.238907:0.363493:0.223434:0.199646:0.223434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo explicas el :@0.199884:0.267535:0.319195:0.267535:0.319195:0.252472:0.199884:0.252472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
concepto de derivada? ¿Qué :@0.153341:0.283377:0.341234:0.283377:0.341234:0.268314:0.153341:0.268314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicaciones tiene el concepto :@0.153341:0.299219:0.352475:0.299219:0.352475:0.284156:0.153341:0.284156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de derivada?:@0.153341:0.315061:0.234026:0.315061:0.234026:0.299998:0.153341:0.299998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.099365:0.307805:0.099365:0.307805:0.083893:0.199646:0.083893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué  es  una  recta  tan-:@0.199884:0.127993:0.361497:0.127993:0.361497:0.112930:0.199884:0.112930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
gente en el punto   a una repre-:@0.153341:0.143835:0.361485:0.143835:0.361485:0.128772:0.153341:0.128772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.271704:0.143940:0.279725:0.143940:0.279725:0.128904:0.271704:0.128904:0.000000
sentación gráfica de una función?  :@0.153341:0.159677:0.365283:0.159677:0.365283:0.144614:0.153341:0.144614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿A qué llamamos pendiente de la :@0.153341:0.175519:0.365300:0.175519:0.365300:0.160455:0.153341:0.160455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recta tangente?:@0.153341:0.191361:0.245583:0.191361:0.245583:0.176297:0.153341:0.176297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.206849:0.290108:0.212480:0.290108:0.212480:0.283794:0.206849:0.283794:0.000000
c:@0.212480:0.291282:0.214094:0.291282:0.214094:0.287601:0.212480:0.287601:0.000000
m:@0.252930:0.296377:0.258560:0.296377:0.258560:0.290063:0.252930:0.290063:0.000000
a:@0.258561:0.297551:0.260601:0.297551:0.260601:0.293870:0.258561:0.293870:0.000000
m:@0.240629:0.312088:0.246259:0.312088:0.246259:0.305774:0.240629:0.305774:0.000000
b:@0.246259:0.313261:0.248346:0.313261:0.248346:0.309580:0.246259:0.309580:0.000000
a:@0.259444:0.286483:0.262943:0.286483:0.262943:0.280169:0.259444:0.280169:0.000000
b:@0.237060:0.319717:0.240640:0.319717:0.240640:0.313403:0.237060:0.313403:0.000000
c:@0.187149:0.289180:0.189917:0.289180:0.189917:0.282866:0.187149:0.282866:0.000000
B:@0.208663:0.261711:0.212286:0.261711:0.212286:0.255397:0.208663:0.255397:0.000000
C:@0.307782:0.316851:0.311630:0.316851:0.311630:0.310537:0.307782:0.310537:0.000000
A:@0.167846:0.318058:0.172194:0.318058:0.172194:0.311744:0.167846:0.311744:0.000000
G:@0.229372:0.294037:0.233720:0.294037:0.233720:0.287723:0.229372:0.287723:0.000000
0:@0.504260:0.326786:0.507470:0.326786:0.507470:0.320472:0.504260:0.320472:0.000000
0:@0.496608:0.319836:0.499818:0.319836:0.499818:0.313522:0.496608:0.313522:0.000000
1:@0.522715:0.328298:0.525925:0.328298:0.525925:0.321984:0.522715:0.321984:0.000000
-1:@0.476065:0.328298:0.481289:0.328298:0.481289:0.321984:0.476065:0.321984:0.000000:0.000000
–2:@0.452320:0.328298:0.459385:0.328298:0.459385:0.321984:0.452320:0.321984:0.000000:0.000000
–3:@0.429495:0.328298:0.436560:0.328298:0.436560:0.321984:0.429495:0.321984:0.000000:0.000000
1:@0.545533:0.328298:0.548743:0.328298:0.548743:0.321984:0.545533:0.321984:0.000000
1:@0.568359:0.328298:0.571569:0.328298:0.571569:0.321984:0.568359:0.321984:0.000000
–1:@0.491463:0.339779:0.498528:0.339779:0.498528:0.333465:0.491463:0.333465:0.000000:0.000000
1:@0.494999:0.306240:0.498209:0.306240:0.498209:0.299926:0.494999:0.299926:0.000000
2:@0.494999:0.289322:0.498209:0.289322:0.498209:0.283008:0.494999:0.283008:0.000000
3:@0.494999:0.271196:0.498209:0.271196:0.498209:0.264882:0.494999:0.264882:0.000000
R:@0.505809:0.268778:0.509563:0.268778:0.509563:0.262464:0.505809:0.262464:0.000000
C:@0.573198:0.319838:0.577046:0.319838:0.577046:0.313524:0.573198:0.313524:0.000000
A:@0.463449:0.316211:0.467796:0.316211:0.467796:0.309897:0.463449:0.309897:0.000000
D:@0.469804:0.295855:0.474318:0.295855:0.474318:0.289541:0.469804:0.289541:0.000000
E:@0.540554:0.295855:0.543663:0.295855:0.543663:0.289541:0.540554:0.289541:0.000000
F:@0.516048:0.319838:0.519062:0.319838:0.519062:0.313524:0.516048:0.313524:0.000000
P:@0.208573:0.460862:0.216695:0.460862:0.216695:0.451742:0.208573:0.451742:0.000000:0.000000
P:@0.328541:0.373031:0.336663:0.373031:0.336663:0.363911:0.328541:0.363911:0.000000:0.000000
P:@0.317802:0.420878:0.325924:0.420878:0.325924:0.411758:0.317802:0.411758:0.000000:0.000000
P:@0.290432:0.445348:0.298554:0.445348:0.298554:0.436227:0.290432:0.436227:0.000000:0.000000
f(a):@0.162157:0.466892:0.175481:0.466892:0.175481:0.457772:0.162157:0.457772:0.000000:0.000000:0.000000:0.000000
f(a+h4):@0.148195:0.441959:0.176601:0.441959:0.176601:0.432839:0.148195:0.432839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(a+h1):@0.148237:0.376697:0.176643:0.376697:0.176643:0.367577:0.148237:0.367577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.211727:0.489248:0.216782:0.489248:0.216782:0.480128:0.211727:0.480128:0.000000
a + h4:@0.274966:0.490458:0.300578:0.490458:0.300578:0.481338:0.274966:0.481338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a + h1:@0.326116:0.491063:0.351728:0.491063:0.351728:0.481943:0.326116:0.481943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.356375:0.414926:0.360792:0.414926:0.360792:0.405806:0.356375:0.405806:0.000000
h:@0.360792:0.416621:0.363837:0.416621:0.363837:0.411304:0.360792:0.411304:0.000000
L:@0.356375:0.404050:0.360792:0.404050:0.360792:0.394929:0.356375:0.394929:0.000000
h:@0.360792:0.405745:0.363837:0.405745:0.363837:0.400428:0.360792:0.400428:0.000000
L:@0.353959:0.369607:0.358376:0.369607:0.358376:0.360487:0.353959:0.360487:0.000000
h:@0.358376:0.371302:0.361421:0.371302:0.361421:0.365985:0.358376:0.365985:0.000000
L:@0.356375:0.424253:0.360792:0.424253:0.360792:0.415133:0.356375:0.415133:0.000000
h:@0.360792:0.425948:0.363837:0.425948:0.363837:0.420631:0.360792:0.420631:0.000000
L:@0.357897:0.451992:0.362314:0.451992:0.362314:0.442872:0.357897:0.442872:0.000000
³:@0.360497:0.423573:0.365888:0.423573:0.365888:0.417259:0.360497:0.417259:0.000000:0.000000:0.000000
²:@0.360497:0.414246:0.365888:0.414246:0.365888:0.407932:0.360497:0.407932:0.000000:0.000000:0.000000
¹:@0.360497:0.403369:0.365888:0.403369:0.365888:0.397055:0.360497:0.397055:0.000000:0.000000:0.000000
y:@0.173020:0.357988:0.177374:0.357988:0.177374:0.348868:0.173020:0.348868:0.000000
x:@0.357835:0.488225:0.362378:0.488225:0.362378:0.478403:0.357835:0.478403:0.000000
P:@0.302859:0.435658:0.310981:0.435658:0.310981:0.426538:0.302859:0.426538:0.000000:0.000000
1:@0.215626:0.570297:0.219549:0.570297:0.219549:0.562580:0.215626:0.562580:0.000000
0:@0.188251:0.572723:0.192174:0.572723:0.192174:0.565006:0.188251:0.565006:0.000000
t:@0.267878:0.579663:0.270562:0.579663:0.270562:0.571946:0.267878:0.571946:0.000000
1:@0.186639:0.593089:0.190563:0.593089:0.190563:0.585372:0.186639:0.585372:0.000000
2:@0.186639:0.610218:0.190563:0.610218:0.190563:0.602501:0.186639:0.602501:0.000000
3:@0.186639:0.627347:0.190563:0.627347:0.190563:0.619630:0.186639:0.619630:0.000000
4:@0.186639:0.644476:0.190563:0.644476:0.190563:0.636759:0.186639:0.636759:0.000000
5:@0.188756:0.661605:0.192679:0.661605:0.192679:0.653888:0.188756:0.653888:0.000000
6:@0.188756:0.678734:0.192679:0.678734:0.192679:0.671017:0.188756:0.671017:0.000000
7:@0.188756:0.695863:0.192679:0.695863:0.192679:0.688146:0.188756:0.688146:0.000000
y:@0.188871:0.709376:0.192555:0.709376:0.192555:0.701659:0.188871:0.701659:0.000000
y = 0,5t + 4,9t²:@0.218274:0.614406:0.266807:0.614406:0.266807:0.606689:0.218274:0.606689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.347497:0.570297:0.351420:0.570297:0.351420:0.562580:0.347497:0.562580:0.000000
0:@0.320122:0.572723:0.324045:0.572723:0.324045:0.565006:0.320122:0.565006:0.000000
t:@0.399749:0.579663:0.402432:0.579663:0.402432:0.571946:0.399749:0.571946:0.000000
1:@0.318510:0.593089:0.322433:0.593089:0.322433:0.585372:0.318510:0.585372:0.000000
2:@0.318510:0.610218:0.322433:0.610218:0.322433:0.602501:0.318510:0.602501:0.000000
3:@0.318510:0.627347:0.322433:0.627347:0.322433:0.619630:0.318510:0.619630:0.000000
4:@0.318510:0.644476:0.322433:0.644476:0.322433:0.636759:0.318510:0.636759:0.000000
5:@0.320626:0.661605:0.324550:0.661605:0.324550:0.653888:0.320626:0.653888:0.000000
6:@0.320626:0.678734:0.324550:0.678734:0.324550:0.671017:0.320626:0.671017:0.000000
7:@0.320626:0.695863:0.324550:0.695863:0.324550:0.688146:0.320626:0.688146:0.000000
v:@0.320733:0.709376:0.324452:0.709376:0.324452:0.701659:0.320733:0.701659:0.000000
y = 0,5t + 9,8t:@0.351455:0.614406:0.397384:0.614406:0.397384:0.606689:0.351455:0.606689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x+h):@0.450682:0.413777:0.469776:0.413777:0.469776:0.407463:0.450682:0.407463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x):@0.455914:0.457012:0.467232:0.457012:0.467232:0.450698:0.455914:0.450698:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.489108:0.478836:0.494159:0.478836:0.494159:0.472522:0.489108:0.472522:0.000000:0.000000
x+h:@0.540323:0.480043:0.553149:0.480043:0.553149:0.473729:0.540323:0.473729:0.000000:0.000000:0.000000:0.000000
p:@0.302154:0.518009:0.313634:0.518009:0.313634:0.507985:0.302154:0.507985:0.000000
 Figura 4.21.:@0.313634:0.518717:0.370994:0.518717:0.370994:0.507240:0.313634:0.507240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.577846:0.297267:0.577846:0.297267:0.562374:0.199644:0.562374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.590414:0.283707:0.590414:0.283707:0.574942:0.199644:0.574942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si se conoce la pendien-:@0.199880:0.614889:0.356377:0.614889:0.356377:0.599826:0.199880:0.599826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
te de una recta y el punto  :@0.153337:0.630731:0.328339:0.630731:0.328339:0.615668:0.153337:0.615668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.153337:0.646678:0.161358:0.646678:0.161358:0.631642:0.153337:0.631642:0.000000
0:@0.161365:0.649566:0.165887:0.649566:0.165887:0.640784:0.161365:0.640784:0.000000
 = ( ,  ), la ecuación carte-:@0.165886:0.646573:0.346525:0.646573:0.346525:0.631510:0.165886:0.631510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.188753:0.646678:0.215622:0.646678:0.215622:0.631642:0.188753:0.631642:0.000000:0.000000:0.000000
0 :@0.195578:0.649566:0.202306:0.649566:0.202306:0.640784:0.195578:0.640784:0.000000:0.000000
0:@0.215621:0.649566:0.220143:0.649566:0.220143:0.640784:0.215621:0.640784:0.000000
siana de la recta que pasa por :@0.153336:0.662415:0.348722:0.662415:0.348722:0.647352:0.153336:0.647352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) y tiene pendiente  está :@0.153336:0.678257:0.361362:0.678257:0.361362:0.663194:0.153336:0.663194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.158771:0.678362:0.183442:0.678362:0.183442:0.663326:0.158771:0.663326:0.000000:0.000000:0.000000
0:@0.165603:0.681250:0.170126:0.681250:0.170126:0.672468:0.165603:0.672468:0.000000
0:@0.183441:0.681250:0.187964:0.681250:0.187964:0.672468:0.183441:0.672468:0.000000
m :@0.314345:0.678362:0.331636:0.678362:0.331636:0.663326:0.314345:0.663326:0.000000:0.000000
dada por :@0.153346:0.694099:0.216158:0.694099:0.216158:0.679036:0.153346:0.679036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(x, y)   :@0.216158:0.694204:0.265709:0.694204:0.265709:0.679168:0.216158:0.679168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.250194:0.694072:0.261927:0.694072:0.261927:0.678191:0.250194:0.678191:0.000000
R:@0.265709:0.693214:0.278409:0.693214:0.278409:0.680937:0.265709:0.680937:0.000000
  tal que   :@0.278409:0.694099:0.342190:0.694099:0.342190:0.679036:0.278409:0.679036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y – y:@0.153346:0.710046:0.184111:0.710046:0.184111:0.695010:0.153346:0.695010:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.184108:0.712934:0.188630:0.712934:0.188630:0.704152:0.184108:0.704152:0.000000
 =  (  –  ).:@0.188631:0.709941:0.268279:0.709941:0.268279:0.694878:0.188631:0.694878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m x x:@0.206063:0.710046:0.255807:0.710046:0.255807:0.695010:0.206063:0.695010:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.255805:0.712934:0.260327:0.712934:0.260327:0.704152:0.255805:0.704152:0.000000
Por otro lado, la ecuación carte-:@0.153346:0.732912:0.359606:0.732912:0.359606:0.717848:0.153346:0.717848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siana de la recta   que pasa por :@0.153346:0.748754:0.359673:0.748754:0.359673:0.733690:0.153346:0.733690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.260238:0.748859:0.267398:0.748859:0.267398:0.733822:0.260238:0.733822:0.000000
los puntos   = ( ,  ), y  :@0.153346:0.764596:0.318277:0.764594:0.318277:0.749531:0.153346:0.749532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.225041:0.764701:0.233062:0.764701:0.233062:0.749664:0.225041:0.749664:0.000000
0:@0.233060:0.767587:0.237583:0.767587:0.237583:0.758806:0.233060:0.758806:0.000000
x y:@0.260450:0.764700:0.287317:0.764700:0.287317:0.749663:0.260450:0.749663:0.000000:0.000000:0.000000
0 :@0.267274:0.767587:0.274001:0.767587:0.274001:0.758806:0.267274:0.758806:0.000000:0.000000
0:@0.287316:0.767587:0.291839:0.767587:0.291839:0.758806:0.287316:0.758806:0.000000
P:@0.153353:0.780542:0.161374:0.780542:0.161374:0.765505:0.153353:0.765505:0.000000
1:@0.161365:0.783429:0.165887:0.783429:0.165887:0.774648:0.161365:0.774648:0.000000
 = ( ,  ) con   ≠   está :@0.165886:0.780436:0.331383:0.780436:0.331383:0.765373:0.165886:0.765373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.188753:0.780542:0.215622:0.780542:0.215622:0.765505:0.188753:0.765505:0.000000:0.000000:0.000000
1 :@0.195578:0.783429:0.202306:0.783429:0.202306:0.774648:0.195578:0.774648:0.000000:0.000000
1:@0.215621:0.783429:0.220143:0.783429:0.220143:0.774648:0.215621:0.774648:0.000000
x:@0.257750:0.780542:0.264575:0.780542:0.264575:0.765505:0.257750:0.765505:0.000000
0:@0.264575:0.783429:0.269097:0.783429:0.269097:0.774648:0.264575:0.774648:0.000000
x:@0.286528:0.780542:0.293353:0.780542:0.293353:0.765505:0.286528:0.765505:0.000000
1:@0.293354:0.783429:0.297876:0.783429:0.297876:0.774648:0.293354:0.774648:0.000000
definida como sigue:  :@0.153338:0.796278:0.294848:0.796278:0.294848:0.781215:0.153338:0.781215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.153338:0.812120:0.158773:0.812120:0.158773:0.797057:0.153338:0.797057:0.000000
x, y:@0.158773:0.812226:0.179107:0.812226:0.179107:0.797189:0.158773:0.797189:0.000000:0.000000:0.000000:0.000000
) :@0.179107:0.812120:0.188325:0.812120:0.188325:0.797057:0.179107:0.797057:0.000000:0.000000
∈:@0.188325:0.812094:0.200057:0.812094:0.200057:0.796212:0.188325:0.796212:0.000000
 :@0.200057:0.812226:0.203839:0.812226:0.203839:0.797189:0.200057:0.797189:0.000000
R:@0.203839:0.811236:0.216539:0.811236:0.216539:0.798958:0.203839:0.798958:0.000000
2:@0.216542:0.806321:0.221065:0.806321:0.221065:0.797539:0.216542:0.797539:0.000000
 tal que:@0.221065:0.812120:0.269718:0.812120:0.269718:0.797057:0.221065:0.797057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.155807:0.853970:0.159588:0.853970:0.159588:0.838906:0.155807:0.838906:0.000000
y y =:@0.166325:0.836111:0.209526:0.836111:0.209526:0.821290:0.166325:0.821290:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.174058:0.836007:0.183508:0.836007:0.183508:0.821159:0.174058:0.821159:0.000000
0:@0.192568:0.838004:0.196994:0.838004:0.196994:0.829410:0.192568:0.829410:0.000000
=:@0.175993:0.926253:0.185789:0.926253:0.185789:0.911431:0.175993:0.911431:0.000000
≠ x:@0.323511:0.836111:0.343848:0.836111:0.343848:0.821290:0.323511:0.821290:0.000000:0.000000:0.000000
y:@0.214329:0.828122:0.221248:0.828122:0.221248:0.813300:0.214329:0.813300:0.000000
1:@0.221263:0.830012:0.225689:0.830012:0.225689:0.821418:0.221263:0.821418:0.000000
–:@0.228142:0.828015:0.237591:0.828015:0.237591:0.813167:0.228142:0.813167:0.000000
y:@0.240626:0.828119:0.247544:0.828119:0.247544:0.813297:0.240626:0.813297:0.000000
0:@0.248166:0.830012:0.252592:0.830012:0.252592:0.821418:0.248166:0.821418:0.000000
x:@0.214336:0.846331:0.221063:0.846331:0.221063:0.831509:0.214336:0.831509:0.000000
1:@0.221263:0.848224:0.225689:0.848224:0.225689:0.839630:0.221263:0.839630:0.000000
–:@0.228142:0.846227:0.237591:0.846227:0.237591:0.831379:0.228142:0.831379:0.000000
x:@0.240244:0.846331:0.246972:0.846331:0.246972:0.831509:0.240244:0.831509:0.000000
0:@0.247789:0.848224:0.252215:0.848224:0.252215:0.839630:0.247789:0.839630:0.000000
x x:@0.262159:0.836111:0.290230:0.836111:0.290230:0.821290:0.262159:0.821290:0.000000:0.000000:0.000000
, x:@0.301137:0.836111:0.316426:0.836111:0.316426:0.821290:0.301137:0.821290:0.000000:0.000000:0.000000
–:@0.271401:0.836007:0.280850:0.836007:0.280850:0.821159:0.271401:0.821159:0.000000
0:@0.291042:0.838004:0.295468:0.838004:0.295468:0.829410:0.291042:0.829410:0.000000
(:@0.256599:0.839310:0.262373:0.839310:0.262373:0.819968:0.256599:0.819968:0.000000
):@0.294536:0.839310:0.300310:0.839310:0.300310:0.819968:0.294536:0.819968:0.000000
1:@0.316626:0.838004:0.321052:0.838004:0.321052:0.829410:0.316626:0.829410:0.000000
0:@0.344660:0.838004:0.349085:0.838004:0.349085:0.829410:0.344660:0.829410:0.000000
.:@0.349700:0.836007:0.352180:0.836007:0.352180:0.821159:0.349700:0.821159:0.000000
y:@0.163171:0.873211:0.170089:0.873211:0.170089:0.858389:0.163171:0.858389:0.000000
1:@0.170095:0.875099:0.174520:0.875099:0.174520:0.866505:0.170095:0.866505:0.000000
–:@0.176973:0.873102:0.186423:0.873102:0.186423:0.858254:0.176973:0.858254:0.000000
y:@0.189457:0.873206:0.196375:0.873206:0.196375:0.858384:0.189457:0.858384:0.000000
0:@0.196997:0.875099:0.201423:0.875099:0.201423:0.866505:0.196997:0.866505:0.000000
x:@0.163168:0.891416:0.169895:0.891416:0.169895:0.876595:0.163168:0.876595:0.000000
1:@0.170095:0.893309:0.174520:0.893309:0.174520:0.884715:0.170095:0.884715:0.000000
–:@0.176973:0.891312:0.186423:0.891312:0.186423:0.876464:0.176973:0.876464:0.000000
x:@0.189076:0.891416:0.195803:0.891416:0.195803:0.876595:0.189076:0.876595:0.000000
0:@0.196620:0.893309:0.201046:0.893309:0.201046:0.884715:0.196620:0.884715:0.000000
m:@0.160765:0.926248:0.174081:0.926248:0.174081:0.911426:0.160765:0.911426:0.000000
df:@0.190310:0.918297:0.202101:0.918297:0.202101:0.903475:0.190310:0.903475:0.000000:0.000000
dx:@0.189742:0.936467:0.204393:0.936467:0.204393:0.921646:0.189742:0.921646:0.000000:0.000000
El número real :@0.153344:0.883212:0.250617:0.883212:0.250617:0.868149:0.153344:0.868149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y y =:@0.259244:0.834483:0.304455:0.834483:0.304455:0.818972:0.259244:0.818972:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.267337:0.834374:0.277226:0.834374:0.277226:0.818836:0.267337:0.818836:0.000000
0:@0.286708:0.836464:0.291339:0.836464:0.291339:0.827471:0.286708:0.827471:0.000000
=:@0.269363:0.928814:0.279615:0.928814:0.279615:0.913303:0.269363:0.913303:0.000000
≠ x:@0.423738:0.834483:0.445019:0.834483:0.445019:0.818972:0.423738:0.818972:0.000000:0.000000:0.000000
y:@0.309481:0.826121:0.316721:0.826121:0.316721:0.810610:0.309481:0.810610:0.000000
1:@0.316735:0.828101:0.321366:0.828101:0.321366:0.819107:0.316735:0.819107:0.000000
–:@0.323934:0.826011:0.333822:0.826011:0.333822:0.810473:0.323934:0.810473:0.000000
y:@0.337000:0.826120:0.344240:0.826120:0.344240:0.810610:0.337000:0.810610:0.000000
0:@0.344889:0.828101:0.349521:0.828101:0.349521:0.819107:0.344889:0.819107:0.000000
x:@0.309488:0.845177:0.316528:0.845177:0.316528:0.829667:0.309488:0.829667:0.000000
1:@0.316735:0.847159:0.321366:0.847159:0.321366:0.838165:0.316735:0.838165:0.000000
–:@0.323934:0.845068:0.333822:0.845068:0.333822:0.829530:0.323934:0.829530:0.000000
x:@0.336599:0.845177:0.343639:0.845177:0.343639:0.829667:0.336599:0.829667:0.000000
0:@0.344495:0.847159:0.349127:0.847159:0.349127:0.838165:0.344495:0.838165:0.000000
x x:@0.359534:0.834483:0.388910:0.834483:0.388910:0.818972:0.359534:0.818972:0.000000:0.000000:0.000000
, x:@0.400323:0.834483:0.416324:0.834483:0.416324:0.818972:0.400323:0.818972:0.000000:0.000000:0.000000
–:@0.369205:0.834374:0.379094:0.834374:0.379094:0.818836:0.369205:0.818836:0.000000
0:@0.389759:0.836464:0.394390:0.836464:0.394390:0.827471:0.389759:0.827471:0.000000
(:@0.353716:0.837831:0.359758:0.837831:0.359758:0.817591:0.353716:0.817591:0.000000
):@0.393416:0.837831:0.399459:0.837831:0.399459:0.817591:0.393416:0.817591:0.000000
1:@0.416531:0.836464:0.421162:0.836464:0.421162:0.827471:0.416531:0.827471:0.000000
0:@0.445868:0.836464:0.450499:0.836464:0.450499:0.827471:0.445868:0.827471:0.000000
.:@0.451145:0.834374:0.453739:0.834374:0.453739:0.818836:0.451145:0.818836:0.000000
y:@0.255944:0.873307:0.263184:0.873307:0.263184:0.857797:0.255944:0.857797:0.000000
1:@0.263189:0.875282:0.267821:0.875282:0.267821:0.866289:0.263189:0.866289:0.000000
–:@0.270388:0.873193:0.280277:0.873193:0.280277:0.857655:0.270388:0.857655:0.000000
y:@0.283452:0.873302:0.290692:0.873302:0.290692:0.857791:0.283452:0.857791:0.000000
0:@0.291343:0.875282:0.295975:0.875282:0.295975:0.866289:0.291343:0.866289:0.000000
x:@0.255941:0.892360:0.262981:0.892360:0.262981:0.876849:0.255941:0.876849:0.000000
1:@0.263189:0.894340:0.267821:0.894340:0.267821:0.885347:0.263189:0.885347:0.000000
–:@0.270388:0.892251:0.280277:0.892251:0.280277:0.876713:0.270388:0.876713:0.000000
x:@0.283053:0.892360:0.290093:0.892360:0.290093:0.876849:0.283053:0.876849:0.000000
0:@0.290948:0.894340:0.295579:0.894340:0.295579:0.885347:0.290948:0.885347:0.000000
m:@0.253426:0.928810:0.267361:0.928810:0.267361:0.913299:0.253426:0.913299:0.000000
df:@0.284345:0.920489:0.296683:0.920489:0.296683:0.904978:0.284345:0.904978:0.000000:0.000000
dx:@0.283750:0.939504:0.299082:0.939504:0.299082:0.923994:0.283750:0.923994:0.000000:0.000000
es la pendiente de la recta.:@0.153344:0.909746:0.324843:0.909746:0.324843:0.894683:0.153344:0.894683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000