119:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento numérico y variacional:@0.603971:0.043660:0.926928:0.043660:0.926928:0.024915:0.603971:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.1 Derivada de la función cuadrática :@0.073089:0.136836:0.367577:0.136836:0.367577:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,  ,       con   ≠ 0. La función cuadrática está definida como sigue: :@0.073089:0.164198:0.618459:0.164198:0.618459:0.147764:0.073089:0.147764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.112499:0.164198:0.152663:0.164198:0.152663:0.147792:0.112499:0.147792:0.000000:0.000000:0.000000:0.000000:0.000000
∈ ℝ:@0.156915:0.164781:0.190141:0.164781:0.190141:0.147126:0.156915:0.147126:0.000000:0.000000:0.000000
a:@0.225575:0.164198:0.234833:0.164198:0.234833:0.147792:0.225575:0.147792:0.000000
f x:@0.296498:0.187982:0.313377:0.187982:0.313377:0.171576:0.296498:0.171576:0.000000:0.000000:0.000000
( ) = :@0.301118:0.187982:0.336994:0.187982:0.336994:0.171548:0.301118:0.171548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.336883:0.187982:0.353523:0.187982:0.353523:0.171576:0.336883:0.171576:0.000000:0.000000
2:@0.353497:0.181925:0.358734:0.181925:0.358734:0.172344:0.353497:0.172344:0.000000
 +   +  ,        .:@0.358686:0.187988:0.482917:0.187988:0.482917:0.171555:0.358686:0.171555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx:@0.377480:0.187988:0.393955:0.187988:0.393955:0.171582:0.377480:0.171582:0.000000:0.000000
c x:@0.412693:0.187988:0.442697:0.187988:0.442697:0.171582:0.412693:0.171582:0.000000:0.000000:0.000000
∈ ℝ:@0.446581:0.188571:0.479806:0.188571:0.479806:0.170917:0.446581:0.170917:0.000000:0.000000:0.000000
Calculemos :@0.073098:0.227402:0.161611:0.227402:0.161611:0.210968:0.073098:0.210968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
df:@0.166372:0.219033:0.180251:0.219033:0.180251:0.202627:0.166372:0.202627:0.000000:0.000000
dx:@0.164992:0.239003:0.181632:0.239003:0.181632:0.222597:0.164992:0.222597:0.000000:0.000000
 ( ) o  ( ). Para el efecto, estudiemos el límite del cociente incremental.:@0.185092:0.227409:0.693639:0.227409:0.693639:0.210976:0.185092:0.210976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.193836:0.227409:0.201291:0.227409:0.201291:0.211003:0.193836:0.211003:0.000000
f' x:@0.223619:0.227409:0.244529:0.227409:0.244529:0.211003:0.223619:0.211003:0.000000:0.000000:0.000000:0.000000
Para     y   ≠ 0, de la definición de la función  , se tiene: :@0.073066:0.254771:0.500703:0.254771:0.500703:0.238338:0.073066:0.238338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x:@0.103567:0.254771:0.114261:0.254771:0.114261:0.238365:0.103567:0.238365:0.000000:0.000000
∈ ℝ :@0.118164:0.255354:0.155899:0.255354:0.155899:0.237700:0.118164:0.237700:0.000000:0.000000:0.000000:0.000000
h:@0.167771:0.254771:0.177269:0.254771:0.177269:0.238365:0.167771:0.238365:0.000000
f:@0.425270:0.254771:0.429964:0.254771:0.429964:0.238365:0.425270:0.238365:0.000000
f x:@0.073066:0.278555:0.089945:0.278555:0.089945:0.262149:0.073066:0.262149:0.000000:0.000000:0.000000
(  +  ) =  (  +  )  +  (  +  ) + :@0.077686:0.278555:0.293374:0.278555:0.293374:0.262121:0.077686:0.262121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.108666:0.278555:0.118164:0.278555:0.118164:0.262149:0.108666:0.262149:0.000000
a x:@0.141670:0.278555:0.163114:0.278555:0.163114:0.262149:0.141670:0.262149:0.000000:0.000000:0.000000
h:@0.181834:0.278555:0.191333:0.278555:0.191333:0.262149:0.181834:0.262149:0.000000
2:@0.196112:0.272492:0.201349:0.272492:0.201349:0.262910:0.196112:0.262910:0.000000
b x:@0.220095:0.278555:0.241539:0.278555:0.241539:0.262149:0.220095:0.262149:0.000000:0.000000:0.000000
h:@0.260259:0.278555:0.269757:0.278555:0.269757:0.262149:0.260259:0.262149:0.000000
c:@0.293264:0.278555:0.300921:0.278555:0.300921:0.262149:0.293264:0.262149:0.000000
 :@0.073089:0.298771:0.076402:0.298771:0.076402:0.282365:0.073089:0.282365:0.000000
= a x:@0.129986:0.298771:0.165587:0.298771:0.165587:0.282365:0.129986:0.282365:0.000000:0.000000:0.000000:0.000000:0.000000
(  + 2  +  ) +  (  +  ) + :@0.153328:0.298771:0.345488:0.298771:0.345488:0.282338:0.153328:0.282338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.165514:0.292707:0.170751:0.292707:0.170751:0.283127:0.165514:0.283127:0.000000
xh:@0.198388:0.298771:0.215267:0.298771:0.215267:0.282365:0.198388:0.282365:0.000000:0.000000
h:@0.234006:0.298771:0.243504:0.298771:0.243504:0.282365:0.234006:0.282365:0.000000
2:@0.243440:0.292707:0.248677:0.292707:0.248677:0.283127:0.243440:0.283127:0.000000
b x:@0.272209:0.298771:0.293653:0.298771:0.293653:0.282365:0.272209:0.282365:0.000000:0.000000:0.000000
h:@0.312374:0.298771:0.321872:0.298771:0.321872:0.282365:0.312374:0.282365:0.000000
c:@0.345378:0.298771:0.353035:0.298771:0.353035:0.282365:0.345378:0.282365:0.000000
 :@0.073089:0.318987:0.076402:0.318987:0.076402:0.302581:0.073089:0.302581:0.000000
= ax:@0.129986:0.318987:0.160763:0.318987:0.160763:0.302581:0.129986:0.302581:0.000000:0.000000:0.000000:0.000000
2:@0.160716:0.312923:0.165953:0.312923:0.165953:0.303343:0.160716:0.303343:0.000000
 + 2:@0.165907:0.318987:0.193702:0.318987:0.193702:0.302554:0.165907:0.302554:0.000000:0.000000:0.000000:0.000000
axh:@0.193592:0.318987:0.219656:0.318987:0.219656:0.302581:0.193592:0.302581:0.000000:0.000000:0.000000
 + :@0.219601:0.318987:0.238487:0.318987:0.238487:0.302554:0.219601:0.302554:0.000000:0.000000:0.000000
ah:@0.238395:0.318987:0.257078:0.318987:0.257078:0.302581:0.238395:0.302581:0.000000:0.000000
2:@0.257026:0.312923:0.262263:0.312923:0.262263:0.303343:0.257026:0.303343:0.000000
 +   + :@0.262217:0.318987:0.316316:0.318987:0.316316:0.302554:0.262217:0.302554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx:@0.281011:0.318987:0.297485:0.318987:0.297485:0.302581:0.281011:0.302581:0.000000:0.000000
bh:@0.316224:0.318987:0.334907:0.318987:0.334907:0.302581:0.316224:0.302581:0.000000:0.000000
 + :@0.334852:0.318987:0.353738:0.318987:0.353738:0.302554:0.334852:0.302554:0.000000:0.000000:0.000000
c:@0.353646:0.318987:0.361303:0.318987:0.361303:0.302581:0.353646:0.302581:0.000000
 :@0.073089:0.339202:0.076402:0.339202:0.076402:0.322796:0.073089:0.322796:0.000000
= ax:@0.129986:0.339202:0.160763:0.339202:0.160763:0.322796:0.129986:0.322796:0.000000:0.000000:0.000000:0.000000
2:@0.160716:0.333138:0.165953:0.333138:0.165953:0.323557:0.160716:0.323557:0.000000
 +   +   +  (2:@0.165907:0.339202:0.269503:0.339202:0.269503:0.322768:0.165907:0.322768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx:@0.184701:0.339202:0.201175:0.339202:0.201175:0.322796:0.184701:0.322796:0.000000:0.000000
c:@0.219914:0.339202:0.227571:0.339202:0.227571:0.322796:0.219914:0.322796:0.000000
h ax  b:@0.246292:0.339202:0.313331:0.339202:0.313331:0.322796:0.246292:0.322796:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+   + :@0.289236:0.339202:0.332143:0.339202:0.332143:0.322768:0.289236:0.322768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ah:@0.332051:0.339202:0.350734:0.339202:0.350734:0.322796:0.332051:0.322796:0.000000:0.000000
):@0.350679:0.339202:0.355557:0.339202:0.355557:0.322768:0.350679:0.322768:0.000000
 :@0.073089:0.359418:0.076402:0.359418:0.076402:0.343012:0.073089:0.343012:0.000000
= f x   h ax  b:@0.129986:0.359418:0.250868:0.359418:0.250868:0.343012:0.129986:0.343012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) +  (2:@0.148763:0.359418:0.207041:0.359418:0.207041:0.342984:0.148763:0.342984:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+   + :@0.226773:0.359418:0.269680:0.359418:0.269680:0.342984:0.226773:0.342984:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ah:@0.269588:0.359418:0.288272:0.359418:0.288272:0.343012:0.269588:0.343012:0.000000:0.000000
).:@0.288217:0.359418:0.296224:0.359418:0.296224:0.342984:0.288217:0.342984:0.000000:0.000000
Luego, :@0.073073:0.397930:0.125962:0.397930:0.125962:0.381496:0.073073:0.381496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.131400:0.391270:0.148280:0.391270:0.148280:0.374864:0.131400:0.374864:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.136020:0.391270:0.219921:0.391270:0.219921:0.374836:0.136020:0.374836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.167000:0.391270:0.176498:0.391270:0.176498:0.374864:0.167000:0.374864:0.000000
f x:@0.198237:0.391270:0.215116:0.391270:0.215116:0.374864:0.198237:0.374864:0.000000:0.000000:0.000000
h:@0.170902:0.411240:0.180400:0.411240:0.180400:0.394834:0.170902:0.394834:0.000000
 = :@0.225369:0.397940:0.242819:0.397940:0.242819:0.381534:0.225369:0.381534:0.000000:0.000000:0.000000
h ax:@0.244725:0.390462:0.284485:0.390462:0.284485:0.374055:0.244725:0.374055:0.000000:0.000000:0.000000:0.000000
(2  +   + :@0.254150:0.390462:0.331295:0.390462:0.331295:0.374028:0.254150:0.374028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.303224:0.390462:0.312482:0.390462:0.312482:0.374055:0.303224:0.374055:0.000000
ah:@0.331203:0.390462:0.349886:0.390462:0.349886:0.374055:0.331203:0.374055:0.000000:0.000000
):@0.349831:0.390462:0.354709:0.390462:0.354709:0.374028:0.349831:0.374028:0.000000
h :@0.294959:0.410432:0.307770:0.410432:0.307770:0.394026:0.294959:0.394026:0.000000:0.000000
 =  ax  b:@0.356568:0.397937:0.426791:0.397937:0.426791:0.381530:0.356568:0.381530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.373963:0.397937:0.382945:0.397937:0.382945:0.381503:0.373963:0.381503:0.000000
+   + :@0.402696:0.397937:0.445604:0.397937:0.445604:0.381503:0.402696:0.381503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ah.:@0.445512:0.397937:0.467453:0.397937:0.467453:0.381530:0.445512:0.381530:0.000000:0.000000:0.000000
Como   es constante, es claro que para | | suficientemente pequeño,     también lo es. :@0.073078:0.436019:0.710431:0.436019:0.710431:0.419585:0.073078:0.419585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.121581:0.436019:0.130840:0.436019:0.130840:0.419613:0.121581:0.419613:0.000000
h:@0.363194:0.436019:0.372693:0.436019:0.372693:0.419613:0.363194:0.419613:0.000000
ah:@0.582830:0.436019:0.601513:0.436019:0.601513:0.419613:0.582830:0.419613:0.000000:0.000000
Entonces,:@0.073078:0.452660:0.143158:0.452660:0.143158:0.436227:0.073078:0.436227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lím:@0.207156:0.473948:0.229208:0.473948:0.229208:0.457542:0.207156:0.457542:0.000000:0.000000:0.000000
 :@0.229153:0.473948:0.233184:0.473948:0.233184:0.457514:0.229153:0.457514:0.000000
f x:@0.238643:0.465833:0.255522:0.465833:0.255522:0.449427:0.238643:0.449427:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.243263:0.465833:0.327163:0.465833:0.327163:0.449399:0.243263:0.449399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.274242:0.465833:0.283740:0.465833:0.283740:0.449427:0.274242:0.449427:0.000000
f x:@0.305479:0.465833:0.322359:0.465833:0.322359:0.449427:0.305479:0.449427:0.000000:0.000000:0.000000
h:@0.278144:0.485803:0.287643:0.485803:0.287643:0.469397:0.278144:0.469397:0.000000
 = :@0.332612:0.473959:0.351497:0.473959:0.351497:0.457526:0.332612:0.457526:0.000000:0.000000:0.000000
lím:@0.351405:0.473959:0.373457:0.473959:0.373457:0.457553:0.351405:0.457553:0.000000:0.000000:0.000000
 :@0.374322:0.473959:0.378354:0.473959:0.378354:0.457526:0.374322:0.457526:0.000000
h ax:@0.382602:0.466704:0.422362:0.466704:0.422362:0.450298:0.382602:0.450298:0.000000:0.000000:0.000000:0.000000
(2  +   + :@0.392027:0.466704:0.469172:0.466704:0.469172:0.450270:0.392027:0.450270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.441101:0.466704:0.450359:0.466704:0.450359:0.450298:0.441101:0.450298:0.000000
ah:@0.469080:0.466704:0.487763:0.466704:0.487763:0.450298:0.469080:0.450298:0.000000:0.000000
):@0.487708:0.466704:0.492586:0.466704:0.492586:0.450270:0.487708:0.450270:0.000000
h:@0.432836:0.486674:0.442334:0.486674:0.442334:0.470268:0.432836:0.470268:0.000000
 = 2  +  ,:@0.496801:0.473957:0.572252:0.473957:0.572252:0.457523:0.496801:0.457523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.524485:0.473957:0.541126:0.473957:0.541126:0.457551:0.524485:0.457551:0.000000:0.000000
b:@0.559864:0.473957:0.569123:0.473957:0.569123:0.457551:0.559864:0.457551:0.000000
Así, la derivada de la función cuadrática es:   ( ) = :@0.073066:0.519694:0.432431:0.519694:0.432431:0.503260:0.073066:0.503260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f' x:@0.388364:0.519694:0.408814:0.519694:0.408814:0.503288:0.388364:0.503288:0.000000:0.000000:0.000000:0.000000
lím :@0.432320:0.519694:0.457612:0.519694:0.457612:0.503288:0.432320:0.503288:0.000000:0.000000:0.000000:0.000000
f x:@0.463124:0.512141:0.480003:0.512141:0.480003:0.495735:0.463124:0.495735:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.467744:0.512141:0.551644:0.512141:0.551644:0.495707:0.467744:0.495707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.498724:0.512141:0.508222:0.512141:0.508222:0.495735:0.498724:0.495735:0.000000
f x:@0.529961:0.512141:0.546840:0.512141:0.546840:0.495735:0.529961:0.495735:0.000000:0.000000:0.000000
h:@0.502626:0.532111:0.512124:0.532111:0.512124:0.515705:0.502626:0.515705:0.000000
 = 2  + :@0.557111:0.519699:0.620267:0.519699:0.620267:0.503265:0.557111:0.503265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.584796:0.519699:0.601436:0.519699:0.601436:0.503293:0.584796:0.503293:0.000000:0.000000
b.:@0.620175:0.519699:0.632323:0.519699:0.632323:0.503293:0.620175:0.503293:0.000000:0.000000
Conclusión:  ( ) = :@0.073056:0.554203:0.202109:0.554203:0.202109:0.537770:0.073056:0.537770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.161613:0.554203:0.178493:0.554203:0.178493:0.537797:0.161613:0.537797:0.000000:0.000000:0.000000
ax:@0.201999:0.554203:0.218639:0.554203:0.218639:0.537797:0.201999:0.537797:0.000000:0.000000
2:@0.218636:0.548137:0.223872:0.548137:0.223872:0.538556:0.218636:0.538556:0.000000
 +   +  ,   :@0.223826:0.554201:0.300493:0.554201:0.300493:0.537767:0.223826:0.537767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx:@0.242620:0.554201:0.259095:0.554201:0.259095:0.537795:0.242620:0.537795:0.000000:0.000000
c:@0.277833:0.554201:0.285491:0.554201:0.285491:0.537795:0.277833:0.537795:0.000000
∀ ∈ ℝ:@0.300382:0.554783:0.357132:0.554783:0.357132:0.537129:0.300382:0.537129:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.312568:0.554201:0.320023:0.554201:0.320023:0.537795:0.312568:0.537795:0.000000
    , la derivada es:   ( ) = 2  + :@0.319949:0.554201:0.561857:0.554201:0.561857:0.537767:0.319949:0.537767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f' x:@0.473521:0.554201:0.493971:0.554201:0.493971:0.537795:0.473521:0.537795:0.000000:0.000000:0.000000:0.000000
ax:@0.526386:0.554201:0.543027:0.554201:0.543027:0.537795:0.526386:0.537795:0.000000:0.000000
b.:@0.561765:0.554201:0.573914:0.554201:0.573914:0.537795:0.561765:0.537795:0.000000:0.000000
Ejercicios resueltos:@0.073108:0.581563:0.216117:0.581563:0.216117:0.564893:0.073108:0.564893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Para  ( ) =  ,  :@0.073089:0.613286:0.201850:0.613286:0.201850:0.596852:0.073089:0.596852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.137749:0.613286:0.154628:0.613286:0.154628:0.596880:0.137749:0.596880:0.000000:0.000000:0.000000
x:@0.178134:0.613286:0.185589:0.613286:0.185589:0.596880:0.178134:0.596880:0.000000
2:@0.185541:0.607222:0.190778:0.607222:0.190778:0.597641:0.185541:0.597641:0.000000
∀ ∈ ℝ:@0.201758:0.613868:0.258507:0.613868:0.258507:0.596214:0.201758:0.596214:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.213943:0.613286:0.221398:0.613286:0.221398:0.596880:0.213943:0.596880:0.000000
    , :@0.221325:0.613286:0.265576:0.613286:0.265576:0.596852:0.221325:0.596852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
df:@0.270393:0.605460:0.284272:0.605460:0.284272:0.589054:0.270393:0.589054:0.000000:0.000000
dx:@0.269013:0.621852:0.285653:0.621852:0.285653:0.605446:0.269013:0.605446:0.000000:0.000000
 ( ) = 2 . Para   = –1, se tiene  '(–1) = –2.:@0.289114:0.613282:0.577077:0.613282:0.577077:0.596848:0.289114:0.596848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.297857:0.613282:0.305312:0.613282:0.305312:0.596876:0.297857:0.596876:0.000000
x:@0.337727:0.613282:0.345182:0.613282:0.345182:0.596876:0.337727:0.596876:0.000000
x:@0.386635:0.613282:0.394090:0.613282:0.394090:0.596876:0.386635:0.596876:0.000000
f :@0.498294:0.613282:0.506227:0.613282:0.506227:0.596876:0.498294:0.596876:0.000000:0.000000
2.  Para  ( ) = 10  – 3  + 1, :@0.073089:0.644113:0.276715:0.644113:0.276715:0.627680:0.073089:0.627680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.137749:0.644113:0.154628:0.644113:0.154628:0.627707:0.137749:0.627707:0.000000:0.000000:0.000000
x:@0.195953:0.644113:0.203408:0.644113:0.203408:0.627707:0.195953:0.627707:0.000000
2:@0.203346:0.638049:0.208583:0.638049:0.208583:0.628469:0.203346:0.628469:0.000000
x:@0.234452:0.644113:0.241907:0.644113:0.241907:0.627707:0.234452:0.627707:0.000000
∀ ∈ ℝ:@0.276605:0.644696:0.333355:0.644696:0.333355:0.627042:0.276605:0.627042:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.288791:0.644113:0.296246:0.644113:0.296246:0.627707:0.288791:0.627707:0.000000
    , :@0.296172:0.644113:0.340423:0.644113:0.340423:0.627680:0.296172:0.627680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
df:@0.345256:0.637182:0.359135:0.637182:0.359135:0.620776:0.345256:0.620776:0.000000:0.000000
dx:@0.343875:0.653574:0.360515:0.653574:0.360515:0.637168:0.343875:0.637168:0.000000:0.000000
 ( ) = 20  – 3.:@0.363976:0.644116:0.458037:0.644116:0.458037:0.627682:0.363976:0.627682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.372719:0.644116:0.380174:0.644116:0.380174:0.627710:0.372719:0.627710:0.000000
x:@0.421499:0.644116:0.428953:0.644116:0.428953:0.627710:0.421499:0.627710:0.000000
Para   = 0,4, :@0.103200:0.675832:0.191960:0.675832:0.191960:0.659399:0.103200:0.659399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.137659:0.675832:0.145114:0.675832:0.145114:0.659426:0.137659:0.659426:0.000000
df:@0.196764:0.668010:0.210643:0.668010:0.210643:0.651603:0.196764:0.651603:0.000000:0.000000
dx:@0.195384:0.684402:0.212024:0.684402:0.212024:0.667996:0.195384:0.667996:0.000000:0.000000
 (0,4) = 5.:@0.215485:0.675831:0.280922:0.675831:0.280922:0.659397:0.215485:0.659397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.    ( ) = –7  + 9,  :@0.073089:0.708449:0.215356:0.708449:0.215356:0.692015:0.073089:0.692015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.105511:0.708449:0.122390:0.708449:0.122390:0.692043:0.105511:0.692043:0.000000:0.000000:0.000000
x:@0.163935:0.708449:0.171390:0.708449:0.171390:0.692043:0.163935:0.692043:0.000000
2:@0.171327:0.702385:0.176564:0.702385:0.176564:0.692804:0.171327:0.692804:0.000000
∀ ∈ ℝ:@0.215227:0.709032:0.271976:0.709032:0.271976:0.691377:0.215227:0.691377:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.227412:0.708449:0.234867:0.708449:0.234867:0.692043:0.227412:0.692043:0.000000
    , :@0.234794:0.708449:0.279045:0.708449:0.279045:0.692015:0.234794:0.692015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
df:@0.283872:0.699730:0.297752:0.699730:0.297752:0.683324:0.283872:0.683324:0.000000:0.000000
dx:@0.282492:0.716122:0.299132:0.716122:0.299132:0.699716:0.282492:0.699716:0.000000:0.000000
 ( ) = –14 , :@0.302593:0.708453:0.383769:0.708453:0.383769:0.692019:0.302593:0.692019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.311336:0.708453:0.318791:0.708453:0.318791:0.692047:0.311336:0.692047:0.000000
x:@0.369227:0.708453:0.376682:0.708453:0.376682:0.692047:0.369227:0.692047:0.000000
df:@0.388623:0.699909:0.402502:0.699909:0.402502:0.683503:0.388623:0.683503:0.000000:0.000000
dx:@0.387243:0.716301:0.403883:0.716301:0.403883:0.699895:0.387243:0.699895:0.000000:0.000000
 (0) = 0.:@0.407343:0.708452:0.460743:0.708452:0.460743:0.692018:0.407343:0.692018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.    ( ) = – :@0.073089:0.745711:0.159094:0.745711:0.159094:0.729277:0.073089:0.729277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.105511:0.745711:0.122390:0.745711:0.122390:0.729304:0.105511:0.729304:0.000000:0.000000:0.000000
5:@0.161610:0.737705:0.170593:0.737705:0.170593:0.721271:0.161610:0.721271:0.000000
2 :@0.161610:0.754097:0.174624:0.754097:0.174624:0.737663:0.161610:0.737663:0.000000:0.000000
x:@0.173133:0.745707:0.180588:0.745707:0.180588:0.729301:0.173133:0.729301:0.000000
2:@0.180524:0.739647:0.185761:0.739647:0.185761:0.730066:0.180524:0.730066:0.000000
 + 0,1 , :@0.185715:0.745711:0.239980:0.745711:0.239980:0.729277:0.185715:0.729277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.225438:0.745711:0.232893:0.745711:0.232893:0.729304:0.225438:0.729304:0.000000
df:@0.244809:0.736812:0.258688:0.736812:0.258688:0.720406:0.244809:0.720406:0.000000:0.000000
dx:@0.243428:0.753204:0.260069:0.753204:0.260069:0.736798:0.243428:0.736798:0.000000:0.000000
 ( ) = –5  + 0,1, :@0.263529:0.745716:0.375574:0.745716:0.375574:0.729282:0.263529:0.729282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.272273:0.745716:0.279728:0.745716:0.279728:0.729309:0.272273:0.729309:0.000000
x:@0.321273:0.745716:0.328728:0.745716:0.328728:0.729309:0.321273:0.729309:0.000000
df:@0.380375:0.735918:0.394254:0.735918:0.394254:0.719512:0.380375:0.719512:0.000000:0.000000
dx:@0.378994:0.752311:0.395635:0.752311:0.395635:0.735904:0.378994:0.735904:0.000000:0.000000
1:@0.415980:0.735918:0.424962:0.735918:0.424962:0.719484:0.415980:0.719484:0.000000
50:@0.411525:0.752311:0.429417:0.752311:0.429417:0.735877:0.411525:0.735877:0.000000:0.000000
 = 0.:@0.437725:0.745711:0.468650:0.745711:0.468650:0.729277:0.437725:0.729277:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.350107:0.482652:0.356583:0.482652:0.356583:0.471466:0.350107:0.471466:0.000000
→:@0.356538:0.482091:0.367273:0.482091:0.367273:0.472053:0.356538:0.472053:0.000000
0:@0.367217:0.482652:0.373342:0.482652:0.373342:0.471447:0.367217:0.471447:0.000000
h:@0.432642:0.527680:0.439118:0.527680:0.439118:0.516494:0.432642:0.516494:0.000000
→:@0.439074:0.527121:0.449810:0.527121:0.449810:0.517083:0.439074:0.517083:0.000000
0:@0.449754:0.527682:0.455878:0.527682:0.455878:0.516477:0.449754:0.516477:0.000000
h:@0.205912:0.482655:0.212388:0.482655:0.212388:0.471469:0.205912:0.471469:0.000000
→:@0.212337:0.482091:0.223072:0.482091:0.223072:0.472053:0.212337:0.472053:0.000000
0:@0.223016:0.482652:0.229141:0.482652:0.229141:0.471447:0.223016:0.471447:0.000000
De la primera derivada obtenemos los intervalos de crecimiento y decrecimiento de la :@0.087319:0.791004:0.655303:0.791004:0.655303:0.776064:0.087319:0.776064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función y los posibles máximos y mínimos relativos. :@0.087319:0.806133:0.427616:0.806133:0.427616:0.791193:0.087319:0.791193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El límite:@0.087319:0.828410:0.138896:0.828410:0.138896:0.813471:0.087319:0.813471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.360945:0.832678:0.377065:0.832678:0.377065:0.817018:0.360945:0.817018:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.365363:0.832678:0.445450:0.832678:0.445450:0.816991:0.365363:0.816991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.394934:0.832678:0.404001:0.832678:0.404001:0.817018:0.394934:0.817018:0.000000
f x:@0.424752:0.832678:0.440864:0.832678:0.440864:0.817018:0.424752:0.817018:0.000000:0.000000:0.000000
h:@0.398659:0.851211:0.407726:0.851211:0.407726:0.835551:0.398659:0.835551:0.000000
h:@0.329236:0.844684:0.335149:0.844684:0.335149:0.834471:0.329236:0.834471:0.000000
→:@0.335107:0.844172:0.344909:0.844172:0.344909:0.835006:0.335107:0.835006:0.000000
0:@0.344857:0.844684:0.350449:0.844684:0.350449:0.834453:0.344857:0.834453:0.000000
lím:@0.330990:0.835264:0.350970:0.835264:0.350970:0.820349:0.330990:0.820349:0.000000:0.000000:0.000000
 ,:@0.448579:0.841013:0.455055:0.841013:0.455055:0.826073:0.448579:0.826073:0.000000:0.000000
se usa para definir la derivada de una función de   en  . Si el límite existe, este   se denota :@0.087328:0.870439:0.671926:0.870439:0.671926:0.855499:0.087328:0.855499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.407330:0.870439:0.411597:0.870439:0.411597:0.855524:0.407330:0.855524:0.000000
x:@0.435476:0.870439:0.442254:0.870439:0.442254:0.855524:0.435476:0.855524:0.000000
y:@0.592925:0.870439:0.599719:0.870439:0.599719:0.855524:0.592925:0.855524:0.000000
con  ( ) o también con :@0.087311:0.891266:0.242384:0.891266:0.242384:0.876326:0.087311:0.876326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f' x:@0.115876:0.891266:0.134367:0.891266:0.134367:0.876351:0.115876:0.876351:0.000000:0.000000:0.000000:0.000000
df:@0.244737:0.883679:0.258616:0.883679:0.258616:0.867273:0.244737:0.867273:0.000000:0.000000
dx:@0.243356:0.900069:0.259997:0.900069:0.259997:0.883662:0.243356:0.883662:0.000000:0.000000
 ( ). Esto se lee \  prima de  \.:@0.261059:0.891264:0.446270:0.891264:0.446270:0.876324:0.261059:0.876324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.268941:0.891264:0.275718:0.891264:0.275718:0.876349:0.268941:0.876349:0.000000
f:@0.363102:0.891264:0.367369:0.891264:0.367369:0.876349:0.363102:0.876349:0.000000
x:@0.433502:0.891264:0.440279:0.891264:0.440279:0.876349:0.433502:0.876349:0.000000
f' x:@0.305739:0.926829:0.324230:0.926829:0.324230:0.911915:0.305739:0.911915:0.000000:0.000000:0.000000:0.000000
( ) = :@0.313118:0.926829:0.345565:0.926829:0.345565:0.911889:0.313118:0.911889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.380065:0.918166:0.396184:0.918166:0.396184:0.902505:0.380065:0.902505:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.384482:0.918166:0.464568:0.918166:0.464568:0.902479:0.384482:0.902479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.414053:0.918166:0.423119:0.918166:0.423119:0.902505:0.414053:0.902505:0.000000
f x:@0.443870:0.918166:0.459982:0.918166:0.459982:0.902505:0.443870:0.902505:0.000000:0.000000:0.000000
h:@0.417778:0.936699:0.426844:0.936699:0.426844:0.921038:0.417778:0.921038:0.000000
h:@0.349424:0.929306:0.355337:0.929306:0.355337:0.919092:0.349424:0.919092:0.000000
→:@0.355296:0.928793:0.365098:0.928793:0.365098:0.919628:0.355296:0.919628:0.000000
0:@0.365045:0.929306:0.370637:0.929306:0.370637:0.919075:0.365045:0.919075:0.000000
lím:@0.352070:0.919249:0.372050:0.919249:0.372050:0.904334:0.352070:0.904334:0.000000:0.000000:0.000000
 .:@0.467199:0.926826:0.473675:0.926826:0.473675:0.911886:0.467199:0.911886:0.000000:0.000000
Simbología matemática :@0.749356:0.429620:0.908654:0.428573:0.908487:0.414177:0.749190:0.415224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  , y    . La distancia :@0.743376:0.451180:0.911100:0.450077:0.910935:0.435885:0.743211:0.436988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.777410:0.450956:0.783848:0.450914:0.783684:0.436746:0.777246:0.436788:0.000000
∈ ℝ:@0.800227:0.451309:0.828285:0.451125:0.828108:0.435879:0.800051:0.436063:0.000000:0.000000:0.000000
de   a   se denota  ( ,  ), y :@0.743526:0.465552:0.910376:0.464455:0.910212:0.450263:0.743362:0.451360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.763158:0.465423:0.789960:0.465247:0.789796:0.451079:0.762994:0.451255:0.000000:0.000000:0.000000
d x y:@0.858680:0.464795:0.889695:0.464591:0.889531:0.450423:0.858516:0.450627:0.000000:0.000000:0.000000:0.000000:0.000000
se lee “distancia de   a  \.:@0.743677:0.479924:0.895870:0.478923:0.895706:0.464731:0.743512:0.465732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.863314:0.479138:0.890115:0.478961:0.889951:0.464793:0.863150:0.464969:0.000000:0.000000:0.000000
El conjunto de todas las :@0.743869:0.497865:0.896170:0.496864:0.896006:0.482672:0.743704:0.483673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones polinomiales de :@0.744035:0.512237:0.912936:0.511127:0.912771:0.496934:0.743871:0.498045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
grado ≤ 4 con coeficientes :@0.744202:0.526609:0.914679:0.525488:0.914515:0.511296:0.744037:0.512417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales se denota con  [ ].:@0.744368:0.540981:0.912756:0.539878:0.912591:0.525686:0.744204:0.526789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.876293:0.540114:0.883860:0.540064:0.883696:0.525895:0.876129:0.525945:0.000000
4 :@0.883850:0.540287:0.890366:0.540244:0.890270:0.531970:0.883755:0.532013:0.000000:0.000000
ℝ:@0.894449:0.540502:0.905926:0.540426:0.905750:0.525180:0.894272:0.525256:0.000000
El cociente incremental de :@0.744635:0.558926:0.914661:0.557808:0.914497:0.543616:0.744471:0.544734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función polinomial   en :@0.744802:0.573298:0.911652:0.572201:0.911487:0.558009:0.744638:0.559106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.880653:0.572405:0.888649:0.572352:0.888485:0.558184:0.880489:0.558236:0.000000
el punto   se denota  ( ). :@0.744968:0.587670:0.910992:0.586578:0.910827:0.572386:0.744804:0.573478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.801401:0.587299:0.809397:0.587246:0.809233:0.573078:0.801237:0.573131:0.000000
Q h:@0.878118:0.586794:0.900659:0.586646:0.900495:0.572478:0.877953:0.572626:0.000000:0.000000:0.000000
Cuando      [ ],       :@0.745135:0.602042:0.908943:0.600970:0.908779:0.586778:0.744971:0.587849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.798356:0.601692:0.806352:0.601639:0.806188:0.587471:0.798192:0.587524:0.000000
∈:@0.809712:0.602120:0.822954:0.602033:0.822777:0.586787:0.809536:0.586874:0.000000
P:@0.826287:0.601508:0.833853:0.601458:0.833689:0.587290:0.826122:0.587340:0.000000
4 :@0.833786:0.601682:0.840301:0.601640:0.840205:0.593365:0.833690:0.593408:0.000000:0.000000
ℝ:@0.844410:0.601898:0.855887:0.601822:0.855710:0.586576:0.844233:0.586652:0.000000
a:@0.866055:0.601252:0.874051:0.601200:0.873887:0.587031:0.865891:0.587084:0.000000
∈ ℝ:@0.877411:0.601681:0.905468:0.601496:0.905291:0.586250:0.877234:0.586435:0.000000:0.000000:0.000000
fijo,      , tal que   ≠ 0. :@0.745312:0.616419:0.900844:0.615396:0.900679:0.601204:0.745148:0.602227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.770206:0.616255:0.778409:0.616201:0.778245:0.602033:0.770042:0.602087:0.000000
∈ ℝ:@0.781769:0.616682:0.809826:0.616498:0.809650:0.601252:0.781592:0.601436:0.000000:0.000000:0.000000
h:@0.862517:0.615649:0.870720:0.615595:0.870556:0.601426:0.862353:0.601480:0.000000
De la función polinomial :@0.740294:0.187395:0.906069:0.187395:0.906069:0.172455:0.740294:0.172455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tenemos, entre otros, estos :@0.740294:0.202524:0.921418:0.202524:0.921418:0.187584:0.740294:0.187584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tres tipos::@0.740294:0.217652:0.803524:0.217652:0.803524:0.202713:0.740294:0.202713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Lineal:@0.740294:0.239930:0.783501:0.239930:0.783501:0.224524:0.740294:0.224524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, definida por:@0.783417:0.239930:0.870132:0.239930:0.870132:0.224990:0.783417:0.224990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.740294:0.255059:0.755639:0.255059:0.755639:0.240144:0.740294:0.240144:0.000000:0.000000:0.000000
( ) = :@0.744494:0.255059:0.777108:0.255059:0.777108:0.240119:0.744494:0.240119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mx:@0.777008:0.255059:0.797005:0.255059:0.797005:0.240144:0.777008:0.240144:0.000000:0.000000
 +  ,      .:@0.796955:0.255059:0.871487:0.255059:0.871487:0.240119:0.796955:0.240119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b x:@0.814040:0.255059:0.835593:0.255059:0.835593:0.240144:0.814040:0.240144:0.000000:0.000000:0.000000
∈ ℝ:@0.839124:0.255588:0.868659:0.255588:0.868659:0.239539:0.839124:0.239539:0.000000:0.000000:0.000000
Cuadrática:@0.740277:0.277336:0.817363:0.277336:0.817363:0.261930:0.740277:0.261930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, definida por:@0.817286:0.277336:0.904001:0.277336:0.904001:0.262396:0.817286:0.262396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.740277:0.292465:0.755622:0.292465:0.755622:0.277550:0.740277:0.277550:0.000000:0.000000:0.000000
( ) = :@0.744477:0.292465:0.777092:0.292465:0.777092:0.277525:0.744477:0.277525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.776991:0.292465:0.792119:0.292465:0.792119:0.277550:0.776991:0.277550:0.000000:0.000000
2:@0.792095:0.286951:0.796856:0.286951:0.796856:0.278241:0.792095:0.278241:0.000000
 +   +  ,      .:@0.796814:0.292464:0.901903:0.292464:0.901903:0.277524:0.796814:0.277524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx:@0.813899:0.292464:0.828876:0.292464:0.828876:0.277549:0.813899:0.277549:0.000000:0.000000
c x:@0.845911:0.292464:0.866009:0.292464:0.866009:0.277549:0.845911:0.277549:0.000000:0.000000:0.000000
∈ ℝ:@0.869539:0.292993:0.899075:0.292993:0.899075:0.276944:0.869539:0.276944:0.000000:0.000000:0.000000
Cúbica:@0.740304:0.314741:0.789148:0.314741:0.789148:0.299335:0.740304:0.299335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, definida por:@0.789066:0.314741:0.875781:0.314741:0.875781:0.299801:0.789066:0.299801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.740304:0.329870:0.755649:0.329870:0.755649:0.314956:0.740304:0.314956:0.000000:0.000000:0.000000
( ) =   +   +  ,       .:@0.744504:0.329870:0.897144:0.329869:0.897144:0.314929:0.744504:0.314930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.777018:0.329870:0.783795:0.329870:0.783795:0.314956:0.777018:0.314956:0.000000
3:@0.783738:0.324356:0.788499:0.324356:0.788499:0.315646:0.783738:0.315646:0.000000
bx:@0.805542:0.329869:0.820519:0.329869:0.820519:0.314954:0.805542:0.314954:0.000000:0.000000
c x:@0.837554:0.329869:0.861249:0.329869:0.861249:0.314954:0.837554:0.314954:0.000000:0.000000:0.000000
∈ ℝ:@0.864780:0.330398:0.894316:0.330398:0.894316:0.314349:0.864780:0.314349:0.000000:0.000000:0.000000
Competencia :@0.740294:0.146688:0.848854:0.146688:0.848854:0.129741:0.740294:0.129741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.163330:0.837769:0.163330:0.837769:0.146383:0.740294:0.146383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000