:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.º BG:@0.120102:0.967458:0.162238:0.967458:0.162238:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
isposición y compromiso:@0.306727:0.140863:0.485691:0.140863:0.485691:0.125499:0.306727:0.125499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.284763:0.141649:0.297589:0.141649:0.297589:0.124513:0.284763:0.124513:0.000000
¿Cuál es el valor de:@0.117752:0.192000:0.244165:0.192000:0.244165:0.177101:0.117752:0.177101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la derivada de una :@0.121588:0.205830:0.247832:0.205830:0.247832:0.190931:0.121588:0.190931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
constante?:@0.171209:0.219661:0.244164:0.219661:0.244164:0.204762:0.171209:0.204762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.108521:0.163125:0.227756:0.163125:0.227756:0.146224:0.108521:0.146224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nidad de conocimientos:@0.306727:0.340126:0.480398:0.340126:0.480398:0.324762:0.306727:0.324762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.340912:0.297460:0.340912:0.297460:0.323776:0.284892:0.323776:0.000000
Antiderivada o primitiva:@0.287495:0.372146:0.533964:0.372146:0.533964:0.350636:0.287495:0.350636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se dice que   es una antiderivada o primitiva de  , en un intervalo   si  ’( ):@0.287495:0.394927:0.819949:0.394767:0.819949:0.378378:0.287495:0.378538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.375211:0.394927:0.383264:0.394927:0.383264:0.378566:0.375211:0.378566:0.000000
f:@0.636144:0.394927:0.640844:0.394927:0.640844:0.378566:0.636144:0.378566:0.000000
I:@0.761029:0.394927:0.764862:0.394927:0.764862:0.378566:0.761029:0.378566:0.000000
Fx:@0.784918:0.394767:0.813278:0.394767:0.813278:0.378406:0.784918:0.378406:0.000000:0.000000
fx:@0.837215:0.394767:0.858554:0.394767:0.858554:0.378406:0.837215:0.378406:0.000000:0.000000
( ) para :@0.844439:0.394767:0.907683:0.394927:0.907683:0.378538:0.844439:0.378378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.823542:0.394352:0.833659:0.394352:0.833659:0.377410:0.823542:0.377410:0.000000
todo   en el intervalo  .:@0.287500:0.411523:0.453697:0.411523:0.453697:0.395134:0.287500:0.395134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.326751:0.411523:0.334215:0.411523:0.334215:0.395162:0.326751:0.395162:0.000000
I:@0.446658:0.411523:0.450491:0.411523:0.450491:0.395162:0.446658:0.395162:0.000000
Así, por ejemplo, la antiderivada de  () 3:@0.287500:0.435242:0.604618:0.435109:0.604618:0.418720:0.287500:0.418853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx:@0.550349:0.435109:0.571688:0.435109:0.571688:0.418748:0.550349:0.418748:0.000000:0.000000
x:@0.605429:0.435109:0.612892:0.435109:0.612892:0.418748:0.605429:0.418748:0.000000
=:@0.581971:0.434694:0.592088:0.434694:0.592088:0.417752:0.581971:0.417752:0.000000
2:@0.614479:0.427447:0.619690:0.427447:0.619690:0.417949:0.614479:0.417949:0.000000
 puede ser::@0.623222:0.435247:0.703933:0.435247:0.703933:0.418859:0.623222:0.418859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Fx:@0.290008:0.455353:0.313338:0.455353:0.313338:0.438992:0.290008:0.438992:0.000000:0.000000
x:@0.338694:0.455353:0.346157:0.455353:0.346157:0.438992:0.338694:0.438992:0.000000
F x:@0.518253:0.455353:0.541582:0.455353:0.541582:0.438992:0.518253:0.438992:0.000000:0.000000:0.000000
x:@0.566939:0.455353:0.574402:0.455353:0.574402:0.438992:0.566939:0.438992:0.000000
():@0.299222:0.455353:0.320027:0.455353:0.320027:0.438964:0.299222:0.438964:0.000000:0.000000
, porque F’(x) = 3x  o  :@0.354818:0.455353:0.518293:0.455353:0.518293:0.438964:0.354818:0.438964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.527467:0.455353:0.548272:0.455353:0.548272:0.438964:0.527467:0.438964:0.000000:0.000000:0.000000
, 5  porque F’(x) = 3x:@0.607314:0.455353:0.740770:0.455353:0.740770:0.438964:0.607314:0.438964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.323620:0.454938:0.333737:0.454938:0.333737:0.437996:0.323620:0.437996:0.000000
=:@0.551865:0.454938:0.561982:0.454938:0.561982:0.437996:0.551865:0.437996:0.000000
−:@0.586104:0.454938:0.596220:0.454938:0.596220:0.437996:0.586104:0.437996:0.000000
3:@0.347750:0.447692:0.352962:0.447692:0.352962:0.438194:0.347750:0.438194:0.000000
2:@0.488733:0.447692:0.493944:0.447692:0.493944:0.438194:0.488733:0.438194:0.000000
3:@0.576007:0.447692:0.581218:0.447692:0.581218:0.438194:0.576007:0.438194:0.000000
x:@0.732496:0.455353:0.740402:0.455353:0.740402:0.438964:0.732496:0.438964:0.000000
2:@0.741222:0.447692:0.746434:0.447692:0.746434:0.438194:0.741222:0.438194:0.000000
En forma general, una antiderivada de  () 3  se puede escribir como  ():@0.287495:0.475568:0.837845:0.475925:0.837845:0.459536:0.287495:0.459179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx:@0.562380:0.475964:0.583720:0.475964:0.583720:0.459603:0.562380:0.459603:0.000000:0.000000
x:@0.617461:0.475964:0.624924:0.475964:0.624924:0.459603:0.617461:0.459603:0.000000
=:@0.594002:0.475549:0.604119:0.475549:0.604119:0.458607:0.594002:0.458607:0.000000
2:@0.626512:0.468303:0.631724:0.468303:0.631724:0.458805:0.626512:0.458805:0.000000
Fx:@0.807827:0.475925:0.831156:0.475925:0.831156:0.459564:0.807827:0.459564:0.000000:0.000000
x:@0.856512:0.475925:0.863976:0.475925:0.863976:0.459564:0.856512:0.459564:0.000000
C:@0.888816:0.475925:0.898730:0.475925:0.898730:0.459564:0.888816:0.459564:0.000000
=:@0.841439:0.475510:0.851555:0.475510:0.851555:0.458568:0.841439:0.458568:0.000000
+:@0.875677:0.475510:0.885794:0.475510:0.885794:0.458568:0.875677:0.458568:0.000000
3:@0.865570:0.468263:0.870782:0.468263:0.870782:0.458764:0.865570:0.458764:0.000000
.:@0.900434:0.475568:0.903640:0.475568:0.903640:0.459179:0.900434:0.459179:0.000000
Interpretación geométrica:@0.287495:0.504679:0.515583:0.504679:0.515583:0.486242:0.287495:0.486242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Geométricamente, la integral indenida representa una familia de curvas.:@0.287495:0.528090:0.823200:0.528090:0.823200:0.511701:0.287495:0.511701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.542363:0.528090:0.546398:0.528090:0.546398:0.511701:0.542363:0.511701:0.000000
La integral indenida  tiene muchas soluciones, cada una diere de la otra por el valor :@0.287495:0.548255:0.907731:0.548255:0.907731:0.531866:0.287495:0.531866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.403774:0.548255:0.407809:0.548255:0.407809:0.531866:0.403774:0.531866:0.000000
 :@0.721483:0.548255:0.725519:0.548255:0.725519:0.531866:0.721483:0.531866:0.000000
de la constante. Al derivar cada una de las antiderivadas    ():@0.287495:0.564851:0.738710:0.564876:0.738710:0.548487:0.287495:0.548462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Fx:@0.708691:0.564876:0.732020:0.564876:0.732020:0.548515:0.708691:0.548515:0.000000:0.000000
x:@0.757377:0.564876:0.764840:0.564876:0.764840:0.548515:0.757377:0.548515:0.000000
C:@0.789680:0.564876:0.799594:0.564876:0.799594:0.548515:0.789680:0.548515:0.000000
=:@0.742303:0.564462:0.752420:0.564462:0.752420:0.547519:0.742303:0.547519:0.000000
+:@0.776541:0.564462:0.786658:0.564462:0.786658:0.547519:0.776541:0.547519:0.000000
3:@0.766433:0.557214:0.771645:0.557214:0.771645:0.547716:0.766433:0.547716:0.000000
  se obtiene la :@0.801836:0.564846:0.907666:0.564846:0.907666:0.548457:0.801836:0.548457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función  () 3:@0.287502:0.581443:0.404553:0.581205:0.404553:0.564816:0.287502:0.565054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx:@0.350283:0.581205:0.371623:0.581205:0.371623:0.564844:0.350283:0.564844:0.000000:0.000000
x:@0.405364:0.581205:0.412827:0.581205:0.412827:0.564844:0.405364:0.564844:0.000000
=:@0.381905:0.580790:0.392022:0.580790:0.392022:0.563848:0.381905:0.563848:0.000000
2:@0.414415:0.573544:0.419627:0.573544:0.419627:0.564046:0.414415:0.564046:0.000000
.:@0.423156:0.581443:0.426363:0.581443:0.426363:0.565054:0.423156:0.565054:0.000000
Integración indefinida:@0.287495:0.614119:0.480222:0.614119:0.480222:0.595682:0.287495:0.595682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La integral indenida se denota  . La solución general se expresa así::@0.287495:0.639453:0.786122:0.639453:0.786122:0.623064:0.287495:0.623064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.405172:0.639453:0.409208:0.639453:0.409208:0.623064:0.405172:0.623064:0.000000
fx dx:@0.295781:0.660226:0.340210:0.660226:0.340210:0.643865:0.295781:0.643865:0.000000:0.000000:0.000000:0.000000:0.000000
Fx:@0.359228:0.660226:0.382557:0.660226:0.382557:0.643865:0.359228:0.643865:0.000000:0.000000
C:@0.405131:0.660226:0.415045:0.660226:0.415045:0.643865:0.405131:0.643865:0.000000
():@0.302986:0.660226:0.323791:0.660226:0.323791:0.643837:0.302986:0.643837:0.000000:0.000000
():@0.368423:0.660226:0.389228:0.660226:0.389228:0.643837:0.368423:0.643837:0.000000:0.000000
=:@0.345561:0.659806:0.355678:0.659806:0.355678:0.642864:0.345561:0.642864:0.000000
+:@0.391999:0.659806:0.402115:0.659806:0.402115:0.642864:0.391999:0.642864:0.000000
∫:@0.285932:0.666279:0.293506:0.666279:0.293506:0.640866:0.285932:0.640866:0.000000
, donde  ( ) es el integrando,   es la variable de integración,  x) :@0.416660:0.660575:0.907664:0.660575:0.907664:0.644186:0.416660:0.644186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.479553:0.660575:0.496599:0.660575:0.496599:0.644213:0.479553:0.644213:0.000000:0.000000:0.000000
dx:@0.636686:0.660575:0.653418:0.660575:0.653418:0.644213:0.636686:0.644213:0.000000:0.000000
F(:@0.877904:0.660575:0.890840:0.660575:0.890840:0.644213:0.877904:0.644213:0.000000:0.000000
es una antiderivada y   la constante de integración.:@0.287500:0.677171:0.664250:0.677171:0.664250:0.660782:0.287500:0.660782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.446842:0.677171:0.456756:0.677171:0.456756:0.660810:0.446842:0.660810:0.000000
Reglas básicas de integración:@0.287495:0.709846:0.541793:0.709846:0.541793:0.691409:0.287495:0.691409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pienso y progreso:@0.294883:0.286880:0.417347:0.286880:0.417347:0.271515:0.294883:0.271515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En las empresas siempre hay costos fijos, como el arriendo. ¿Qué otro gasto es fijo?:@0.294883:0.304273:0.844487:0.304273:0.844487:0.289374:0.294883:0.289374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una empresa fabrica juguetes educativos, el costo jo inicial cuando no se produce :@0.287495:0.168345:0.907654:0.168345:0.907654:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.666714:0.168345:0.670750:0.168345:0.670750:0.151956:0.666714:0.151956:0.000000
nada es de $1 000, es decir  (0) = 1 000. El departamento de análisis de costos deter-:@0.287495:0.184941:0.903542:0.184941:0.903542:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.486053:0.184941:0.495967:0.184941:0.495967:0.168580:0.486053:0.168580:0.000000
minó que el costo marginal de producir   unidades es::@0.287495:0.201538:0.684589:0.201538:0.684589:0.185149:0.287495:0.185149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.582297:0.201538:0.589760:0.201538:0.589760:0.185177:0.582297:0.185177:0.000000
Cx:@0.541122:0.222014:0.571196:0.222014:0.571196:0.205653:0.541122:0.205653:0.000000:0.000000
x:@0.605784:0.222014:0.613247:0.222014:0.613247:0.205653:0.605784:0.205653:0.000000
’( ) 6:@0.553947:0.222014:0.604402:0.222014:0.604402:0.205625:0.553947:0.205625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.581478:0.221599:0.591595:0.221599:0.591595:0.204657:0.581478:0.204657:0.000000
+:@0.617762:0.221599:0.627879:0.221599:0.627879:0.204657:0.617762:0.204657:0.000000
50:@0.630901:0.222014:0.648794:0.222014:0.648794:0.205625:0.630901:0.205625:0.000000:0.000000
Esto  signica  que,  por  cada  unidad  adicional,  el  costo  varía  según  esa  función. :@0.287495:0.241858:0.907678:0.241858:0.907678:0.225469:0.287495:0.225469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.365085:0.241858:0.369121:0.241858:0.369121:0.225469:0.365085:0.225469:0.000000
La empresa quiere saber cuál es la función del costo total  ( ).:@0.287495:0.258455:0.740089:0.258455:0.740089:0.242066:0.287495:0.242066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C x:@0.709739:0.258455:0.732000:0.258455:0.732000:0.242093:0.709739:0.242093:0.000000:0.000000:0.000000
Integral indenida:@0.286308:0.075160:0.561060:0.075160:0.561060:0.041608:0.286308:0.041608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.485728:0.075160:0.492804:0.075160:0.492804:0.041608:0.485728:0.041608:0.000000
:@0.094760:0.108603:0.183816:0.108603:0.183816:0.011514:0.094760:0.011514:0.000000:0.000000
Regla:@0.358839:0.742002:0.399480:0.742002:0.399480:0.726638:0.358839:0.726638:0.000000:0.000000:0.000000:0.000000:0.000000
Simbología:@0.550403:0.742002:0.632923:0.742002:0.632923:0.726638:0.550403:0.726638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo:@0.777984:0.742002:0.837488:0.742002:0.837488:0.726638:0.777984:0.726638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Integral de una constante :@0.292499:0.763867:0.467508:0.763867:0.467508:0.748968:0.292499:0.748968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por una función:@0.292499:0.778955:0.399547:0.778955:0.399547:0.764056:0.292499:0.764056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
kf xdx:@0.528988:0.769845:0.575708:0.769845:0.575708:0.755120:0.528988:0.755120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k fx:@0.592840:0.769845:0.629476:0.769845:0.629476:0.755120:0.592840:0.755120:0.000000:0.000000:0.000000:0.000000
C:@0.649809:0.769845:0.658731:0.769845:0.658731:0.755120:0.649809:0.755120:0.000000
():@0.542239:0.769845:0.560964:0.769845:0.560964:0.755095:0.542239:0.755095:0.000000:0.000000
():@0.616772:0.769845:0.635496:0.769845:0.635496:0.755095:0.616772:0.755095:0.000000:0.000000
=:@0.580533:0.769472:0.589638:0.769472:0.589638:0.754224:0.580533:0.754224:0.000000
+:@0.637967:0.769472:0.647072:0.769472:0.647072:0.754224:0.637967:0.754224:0.000000
∫:@0.601405:0.775296:0.608222:0.775296:0.608222:0.752424:0.601405:0.752424:0.000000
∫:@0.520131:0.775296:0.526947:0.775296:0.526947:0.752424:0.520131:0.752424:0.000000
3:@0.765688:0.769488:0.773781:0.769488:0.773781:0.754738:0.765688:0.754738:0.000000
3:@0.813369:0.769488:0.821463:0.769488:0.821463:0.754738:0.813369:0.754738:0.000000
xdx:@0.774498:0.769488:0.796245:0.769488:0.796245:0.754763:0.774498:0.754763:0.000000:0.000000:0.000000
xdx:@0.831786:0.769488:0.853538:0.769488:0.853538:0.754763:0.831786:0.754763:0.000000:0.000000:0.000000
=:@0.801072:0.769115:0.810177:0.769115:0.810177:0.753867:0.801072:0.753867:0.000000
∫:@0.821661:0.774940:0.828477:0.774940:0.828477:0.752068:0.821661:0.752068:0.000000
∫:@0.756830:0.774940:0.763647:0.774940:0.763647:0.752068:0.756830:0.752068:0.000000
Integral de una potencia:@0.292494:0.807046:0.456180:0.807046:0.456180:0.792147:0.292494:0.792147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xdx:@0.534700:0.806826:0.563326:0.806826:0.563326:0.792101:0.534700:0.792101:0.000000:0.000000:0.000000
x:@0.584643:0.798799:0.591360:0.798799:0.591360:0.784073:0.584643:0.784073:0.000000
n:@0.582006:0.816723:0.590564:0.816723:0.590564:0.801997:0.582006:0.801997:0.000000
n:@0.542993:0.799931:0.547953:0.799931:0.547953:0.791397:0.542993:0.791397:0.000000
n:@0.592935:0.791903:0.597895:0.791903:0.597895:0.783369:0.592935:0.783369:0.000000
=:@0.568153:0.806453:0.577258:0.806453:0.577258:0.791205:0.568153:0.791205:0.000000
+:@0.593031:0.816354:0.602136:0.816354:0.602136:0.801106:0.593031:0.801106:0.000000
≠−:@0.631335:0.806453:0.653542:0.806453:0.653542:0.791205:0.631335:0.791205:0.000000:0.000000
+:@0.597882:0.791686:0.603159:0.791686:0.603159:0.782849:0.597882:0.782849:0.000000
∫:@0.524570:0.812277:0.531387:0.812277:0.531387:0.789405:0.524570:0.789405:0.000000
1:@0.602688:0.791903:0.607379:0.791903:0.607379:0.783354:0.602688:0.783354:0.000000
1:@0.603819:0.816728:0.611913:0.816728:0.611913:0.801978:0.603819:0.801978:0.000000
1:@0.653474:0.806832:0.661568:0.806832:0.661568:0.792082:0.653474:0.792082:0.000000
; n:@0.610604:0.806826:0.628449:0.806826:0.628449:0.792076:0.610604:0.792076:0.000000:0.000000:0.000000
xdx:@0.745489:0.806826:0.774264:0.806826:0.774264:0.792101:0.745489:0.792101:0.000000:0.000000:0.000000
x:@0.795621:0.798799:0.802338:0.798799:0.802338:0.784073:0.795621:0.784073:0.000000
x:@0.840201:0.798799:0.846918:0.798799:0.846918:0.784073:0.840201:0.784073:0.000000
C:@0.870395:0.806826:0.879318:0.806826:0.879318:0.792101:0.870395:0.792101:0.000000
4:@0.753924:0.799931:0.758615:0.799931:0.758615:0.791382:0.753924:0.791382:0.000000
41:@0.804056:0.791903:0.818502:0.791903:0.818502:0.783354:0.804056:0.783354:0.000000:0.000000
5:@0.848346:0.791903:0.853037:0.791903:0.853037:0.783354:0.848346:0.783354:0.000000
41:@0.793218:0.816728:0.823121:0.816728:0.823121:0.801978:0.793218:0.801978:0.000000:0.000000
5:@0.842973:0.816728:0.851066:0.816728:0.851066:0.801978:0.842973:0.801978:0.000000
=:@0.779083:0.806453:0.788188:0.806453:0.788188:0.791205:0.779083:0.791205:0.000000
+:@0.804243:0.816354:0.813348:0.816354:0.813348:0.801106:0.804243:0.801106:0.000000
=:@0.825306:0.806459:0.834411:0.806459:0.834411:0.791211:0.825306:0.791211:0.000000
+:@0.858575:0.806459:0.867680:0.806459:0.867680:0.791211:0.858575:0.791211:0.000000
+:@0.809003:0.791686:0.814279:0.791686:0.814279:0.782849:0.809003:0.782849:0.000000
∫:@0.735359:0.812277:0.742175:0.812277:0.742175:0.789405:0.735359:0.789405:0.000000
Integral de la función 1/x:@0.292494:0.843577:0.458980:0.843577:0.458980:0.828678:0.292494:0.828678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.547350:0.834104:0.555444:0.834104:0.555444:0.819354:0.547350:0.819354:0.000000
x:@0.547201:0.852028:0.553918:0.852028:0.553918:0.837302:0.547201:0.837302:0.000000
dx:@0.558281:0.842130:0.573290:0.842130:0.573290:0.827405:0.558281:0.827405:0.000000:0.000000
x:@0.606811:0.842130:0.613528:0.842130:0.613528:0.827405:0.606811:0.827405:0.000000
C:@0.633861:0.842130:0.642784:0.842130:0.642784:0.827405:0.633861:0.827405:0.000000
=:@0.578119:0.841757:0.587224:0.841757:0.587224:0.826509:0.578119:0.826509:0.000000
+:@0.622036:0.841757:0.631141:0.841757:0.631141:0.826509:0.622036:0.826509:0.000000
∫:@0.535759:0.847582:0.542576:0.847582:0.542576:0.824710:0.535759:0.824710:0.000000
ln():@0.588389:0.842130:0.619552:0.842130:0.619552:0.827380:0.588389:0.827380:0.000000:0.000000:0.000000:0.000000
1:@0.763511:0.834085:0.771605:0.834085:0.771605:0.819335:0.763511:0.819335:0.000000
x:@0.763362:0.852009:0.770079:0.852009:0.770079:0.837284:0.763362:0.837284:0.000000
dx:@0.774442:0.842113:0.789452:0.842113:0.789452:0.827387:0.774442:0.827387:0.000000:0.000000
x:@0.822972:0.842113:0.829689:0.842113:0.829689:0.827387:0.822972:0.827387:0.000000
C:@0.850022:0.842113:0.858945:0.842113:0.858945:0.827387:0.850022:0.827387:0.000000
=:@0.794281:0.841739:0.803386:0.841739:0.803386:0.826491:0.794281:0.826491:0.000000
+:@0.838197:0.841739:0.847302:0.841739:0.847302:0.826491:0.838197:0.826491:0.000000
∫:@0.751920:0.847563:0.758737:0.847563:0.758737:0.824691:0.751920:0.824691:0.000000
ln():@0.804550:0.842113:0.835713:0.842113:0.835713:0.827363:0.804550:0.827363:0.000000:0.000000:0.000000:0.000000
Integral de la suma y resta :@0.292494:0.886820:0.469492:0.886820:0.469492:0.871921:0.292494:0.871921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de funciones.:@0.292494:0.901907:0.381632:0.901907:0.381632:0.887008:0.292494:0.887008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx:@0.487953:0.892745:0.506731:0.892745:0.506731:0.878020:0.487953:0.878020:0.000000:0.000000
gx dx:@0.527342:0.892745:0.575781:0.892745:0.575781:0.878020:0.527342:0.878020:0.000000:0.000000:0.000000:0.000000:0.000000
fx dx:@0.601921:0.892745:0.641019:0.892745:0.641019:0.878020:0.601921:0.878020:0.000000:0.000000:0.000000:0.000000:0.000000
gx dx:@0.666705:0.892745:0.707311:0.892745:0.707311:0.878020:0.666705:0.878020:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.494310:0.892745:0.512618:0.892745:0.512618:0.877995:0.494310:0.877995:0.000000:0.000000
():@0.535224:0.892745:0.553532:0.892745:0.553532:0.877995:0.535224:0.877995:0.000000:0.000000
():@0.608294:0.892745:0.626602:0.892745:0.626602:0.877995:0.608294:0.877995:0.000000:0.000000
():@0.674587:0.892745:0.692895:0.892745:0.692895:0.877995:0.674587:0.877995:0.000000:0.000000
±:@0.515050:0.892372:0.523953:0.892372:0.523953:0.877124:0.515050:0.877124:0.000000
(:@0.481734:0.893947:0.487134:0.893947:0.487134:0.874460:0.481734:0.874460:0.000000
):@0.554108:0.893947:0.559508:0.893947:0.559508:0.874460:0.554108:0.874460:0.000000
=:@0.580507:0.892372:0.589409:0.892372:0.589409:0.877124:0.580507:0.877124:0.000000
±:@0.644999:0.892372:0.653902:0.892372:0.653902:0.877124:0.644999:0.877124:0.000000
∫:@0.657303:0.898197:0.663968:0.898197:0.663968:0.875325:0.657303:0.875325:0.000000
∫:@0.593256:0.898197:0.599921:0.898197:0.599921:0.875325:0.593256:0.875325:0.000000
∫:@0.473069:0.898197:0.479734:0.898197:0.479734:0.875325:0.473069:0.875325:0.000000
x:@0.739788:0.875338:0.746505:0.875338:0.746505:0.860613:0.739788:0.860613:0.000000
dx:@0.778182:0.875338:0.793192:0.875338:0.793192:0.860613:0.778182:0.860613:0.000000:0.000000
xdx:@0.821204:0.875338:0.842946:0.875338:0.842946:0.860613:0.821204:0.860613:0.000000:0.000000:0.000000
dx:@0.876232:0.875338:0.891241:0.875338:0.891241:0.860613:0.876232:0.860613:0.000000:0.000000
x:@0.739788:0.906780:0.746505:0.906780:0.746505:0.892055:0.739788:0.892055:0.000000
dx:@0.778182:0.906780:0.793192:0.906780:0.793192:0.892055:0.778182:0.892055:0.000000:0.000000
x:@0.812911:0.898751:0.819628:0.898751:0.819628:0.884026:0.812911:0.884026:0.000000
xC:@0.852113:0.906774:0.883658:0.906774:0.883658:0.892049:0.852113:0.892049:0.000000:0.000000
+:@0.750579:0.874965:0.759684:0.874965:0.759684:0.859717:0.750579:0.859717:0.000000
(:@0.732156:0.876539:0.737679:0.876539:0.737679:0.857052:0.732156:0.857052:0.000000
):@0.771031:0.876539:0.776554:0.876539:0.776554:0.857052:0.771031:0.857052:0.000000
=:@0.798025:0.874965:0.807130:0.874965:0.807130:0.859717:0.798025:0.859717:0.000000
+:@0.847033:0.874965:0.856138:0.874965:0.856138:0.859717:0.847033:0.859717:0.000000
+:@0.750579:0.906401:0.759684:0.906401:0.759684:0.891153:0.750579:0.891153:0.000000
(:@0.732156:0.907976:0.737679:0.907976:0.737679:0.888489:0.732156:0.888489:0.000000
):@0.771031:0.907976:0.776554:0.907976:0.776554:0.888489:0.771031:0.888489:0.000000
=:@0.798025:0.906401:0.807130:0.906401:0.807130:0.891153:0.798025:0.891153:0.000000
+:@0.831476:0.906401:0.840582:0.906401:0.840582:0.891153:0.831476:0.891153:0.000000
+:@0.862905:0.906401:0.872010:0.906401:0.872010:0.891153:0.862905:0.891153:0.000000
∫:@0.859605:0.880790:0.866421:0.880790:0.866421:0.857918:0.859605:0.857918:0.000000
∫:@0.811069:0.880790:0.817886:0.880790:0.817886:0.857918:0.811069:0.857918:0.000000
∫:@0.723302:0.880790:0.730118:0.880790:0.730118:0.857918:0.723302:0.857918:0.000000
∫:@0.723297:0.912226:0.730114:0.912226:0.730114:0.889354:0.723297:0.889354:0.000000
3:@0.762404:0.875338:0.770498:0.875338:0.770498:0.860588:0.762404:0.860588:0.000000
3:@0.868464:0.875338:0.876558:0.875338:0.876558:0.860588:0.868464:0.860588:0.000000
3:@0.762404:0.906774:0.770498:0.906774:0.770498:0.892024:0.762404:0.892024:0.000000
2:@0.815645:0.916676:0.823738:0.916676:0.823738:0.901926:0.815645:0.901926:0.000000
3:@0.843303:0.906774:0.851397:0.906774:0.851397:0.892024:0.843303:0.892024:0.000000
2:@0.821064:0.891852:0.825755:0.891852:0.825755:0.883303:0.821064:0.883303:0.000000
©Shutterstock:@0.068421:0.287761:0.068421:0.244936:0.056510:0.244936:0.056510:0.287761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La producción de juguetes :@0.072616:0.428688:0.236729:0.428688:0.236729:0.415279:0.072616:0.415279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
educativos implica cálculo:@0.072616:0.441260:0.230926:0.441260:0.230926:0.427851:0.072616:0.427851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de costos.:@0.072616:0.453832:0.132470:0.453832:0.132470:0.440422:0.072616:0.440422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se considera a la :@0.133690:0.764967:0.248008:0.764967:0.248008:0.750068:0.133690:0.750068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
integración como la :@0.110756:0.778797:0.248008:0.778797:0.248008:0.763898:0.110756:0.763898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
operación inversa de la :@0.090553:0.792628:0.248008:0.792628:0.248008:0.777729:0.090553:0.777729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
derivación y viceversa.:@0.095763:0.806458:0.244338:0.806458:0.244338:0.791559:0.095763:0.791559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para obtener una solución :@0.073934:0.823846:0.248008:0.823846:0.248008:0.808947:0.073934:0.808947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
particular es necesario :@0.098912:0.837677:0.248007:0.837677:0.248007:0.822778:0.098912:0.822778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocer las condiciones :@0.087252:0.851507:0.248007:0.851507:0.248007:0.836608:0.087252:0.836608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iniciales o un punto por :@0.090033:0.865337:0.248008:0.865337:0.248008:0.850438:0.090033:0.850438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
donde pasa la antiderivada, :@0.070064:0.879168:0.248008:0.879168:0.248008:0.864269:0.070064:0.864269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al reemplazar ese punto se :@0.070282:0.892998:0.248007:0.892998:0.248007:0.878099:0.070282:0.878099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
obtiene el valor de la :@0.108461:0.906828:0.248008:0.906828:0.248008:0.891929:0.108461:0.891929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
constante C.:@0.163476:0.920659:0.244340:0.920659:0.244340:0.905760:0.163476:0.905760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
     Matemática:@0.115380:0.732525:0.222921:0.732525:0.222921:0.715624:0.115380:0.715624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–2:@0.147690:0.654706:0.161266:0.654706:0.161266:0.642615:0.147690:0.642615:0.000000:0.000000
–1:@0.147690:0.636570:0.161266:0.636570:0.161266:0.624480:0.147690:0.624480:0.000000:0.000000
1:@0.154391:0.601547:0.161266:0.601547:0.161266:0.589457:0.154391:0.589457:0.000000
2:@0.154391:0.583412:0.161266:0.583412:0.161266:0.571321:0.154391:0.571321:0.000000
3:@0.154391:0.565689:0.161266:0.565689:0.161266:0.553598:0.154391:0.553598:0.000000
4:@0.154391:0.548388:0.161266:0.548388:0.161266:0.536298:0.154391:0.536298:0.000000
5:@0.154391:0.530032:0.161266:0.530032:0.161266:0.517941:0.154391:0.517941:0.000000
–2 –1 0:@0.109883:0.626391:0.160609:0.626391:0.160609:0.614301:0.109883:0.614301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–3:@0.086282:0.626391:0.099859:0.626391:0.099859:0.614301:0.086282:0.614301:0.000000:0.000000
1:@0.184786:0.626391:0.191662:0.626391:0.191662:0.614301:0.184786:0.614301:0.000000
2:@0.208561:0.626391:0.215437:0.626391:0.215437:0.614301:0.208561:0.614301:0.000000
3:@0.232739:0.626391:0.239614:0.626391:0.239614:0.614301:0.232739:0.614301:0.000000
y:@0.155406:0.514459:0.160578:0.514459:0.160578:0.503871:0.155406:0.503871:0.000000
x:@0.253969:0.624781:0.259140:0.624781:0.259140:0.614193:0.253969:0.614193:0.000000
F x:@0.170698:0.666416:0.192261:0.666416:0.192261:0.654316:0.170698:0.654316:0.000000:0.000000:0.000000
: ( ) =   + :@0.176930:0.666416:0.233325:0.666416:0.233325:0.654326:0.176930:0.654326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.209737:0.666416:0.215648:0.666416:0.215648:0.654316:0.209737:0.654316:0.000000
3:@0.215648:0.662018:0.219656:0.662018:0.219656:0.654969:0.215648:0.654969:0.000000
C:@0.233325:0.666416:0.240763:0.666416:0.240763:0.654316:0.233325:0.654316:0.000000
C :@0.122880:0.544267:0.132757:0.544267:0.132757:0.532166:0.122880:0.532166:0.000000:0.000000
= 4:@0.132757:0.544267:0.150461:0.544267:0.150461:0.532177:0.132757:0.532177:0.000000:0.000000:0.000000
C :@0.154200:0.575206:0.164077:0.575206:0.164077:0.563106:0.154200:0.563106:0.000000:0.000000
= 2:@0.164077:0.575206:0.181781:0.575206:0.181781:0.563116:0.164077:0.563116:0.000000:0.000000:0.000000
C :@0.180382:0.654704:0.190259:0.654704:0.190259:0.642604:0.180382:0.642604:0.000000:0.000000
C  C :@0.180382:0.654704:0.190259:0.654704:0.190259:0.642604:0.180382:0.642604:0.000000:0.000000:0.000000:0.000000:0.000000
= –2:@0.190259:0.654704:0.214664:0.654704:0.214664:0.642614:0.190259:0.642614:0.000000:0.000000:0.000000:0.000000
= –2:@0.190259:0.654704:0.214664:0.654704:0.214664:0.642614:0.190259:0.642614:0.000000:0.000000:0.000000:0.000000
= –2:@0.190259:0.654704:0.214664:0.654704:0.214664:0.642614:0.190259:0.642614:0.000000:0.000000:0.000000:0.000000
= –2:@0.190259:0.654704:0.214664:0.654704:0.214664:0.642614:0.190259:0.642614:0.000000:0.000000:0.000000:0.000000
= –2:@0.190259:0.654704:0.214664:0.654704:0.214664:0.642614:0.190259:0.642614:0.000000:0.000000:0.000000:0.000000
C :@0.139262:0.612018:0.147904:0.612018:0.147904:0.601430:0.139262:0.601430:0.000000:0.000000
= 0:@0.147904:0.612018:0.163395:0.612018:0.163395:0.601439:0.147904:0.601439:0.000000:0.000000:0.000000
2 2 2:@0.154391:0.583412:0.161266:0.583412:0.161266:0.571321:0.154391:0.571321:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.133350:0.626391:0.140051:0.626391:0.140051:0.614301:0.133350:0.614301:0.000000
= 2:@0.164077:0.575206:0.181781:0.575206:0.181781:0.563116:0.164077:0.563116:0.000000:0.000000:0.000000
2 2:@0.154391:0.654706:0.161266:0.654706:0.161266:0.642615:0.154391:0.642615:0.000000:0.000000:0.000000
4 4 4:@0.154391:0.548388:0.161266:0.548388:0.161266:0.536298:0.154391:0.536298:0.000000:0.000000:0.000000:0.000000:0.000000
(1, 3):@0.166178:0.557032:0.193156:0.557032:0.193156:0.544942:0.166178:0.544942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000