182:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000
Integración indefinida o primitiva :@0.404235:0.117815:0.836497:0.117815:0.836497:0.073156:0.404235:0.073156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de una función :@0.404235:0.155534:0.596267:0.155534:0.596267:0.110875:0.404235:0.110875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.64. Calcular la integral definida de una función escalonada, identificar sus propiedades cuando los límites de integración son iguales y cuando se intercambian los :@0.148873:0.941316:0.888466:0.941316:0.888466:0.931274:0.148873:0.931274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
límites de integración. :@0.148873:0.950117:0.246050:0.950117:0.246050:0.940075:0.148873:0.940075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.67. Reconocer la derivación y la integración como procesos inversos.:@0.148873:0.958918:0.468455:0.958918:0.468455:0.948876:0.148873:0.948876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.62. Reconocer y graficar las funciones escalonadas para calcular el área encerrada entre la curva y el eje X.:@0.148873:0.967719:0.625111:0.967719:0.625111:0.957677:0.148873:0.957677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Con el propósito de tener una idea acerca de los temas de estudio del :@0.404236:0.188444:0.895837:0.188444:0.895837:0.171946:0.404236:0.171946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cálculo diferencial e integral, presentamos dos problemas que origina-:@0.404236:0.205794:0.891824:0.205794:0.891824:0.189297:0.404236:0.189297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ron el desarrollo de estos temas.:@0.404236:0.223145:0.625066:0.223145:0.625066:0.206647:0.404236:0.206647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Problema 1 :@0.404236:0.256039:0.498405:0.256039:0.498405:0.239093:0.404236:0.239093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Consideremos una función real   definida en el intervalo :@0.491623:0.255577:0.895963:0.255577:0.895963:0.239079:0.491623:0.239079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.722219:0.255692:0.726515:0.255692:0.726515:0.239224:0.722219:0.239224:0.000000
cerrado [ ,  ] de   y asociemos a   el grafo  ( ), esto es,:@0.404236:0.272927:0.796096:0.272934:0.796096:0.256437:0.404236:0.256430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.468621:0.273043:0.493762:0.273043:0.493762:0.256574:0.468621:0.256574:0.000000:0.000000:0.000000
:@0.525758:0.271847:0.539063:0.271847:0.539063:0.258985:0.525758:0.258985:0.000000
f:@0.645925:0.273050:0.650222:0.273050:0.650222:0.256581:0.645925:0.256581:0.000000
G f:@0.710329:0.273050:0.732022:0.273050:0.732022:0.256581:0.710329:0.256581:0.000000:0.000000:0.000000
G f:@0.552144:0.297529:0.573837:0.297529:0.573837:0.281060:0.552144:0.281060:0.000000:0.000000:0.000000
( ) = {( ,  ( )) |     [ ,  ]}.:@0.563587:0.297413:0.743862:0.297413:0.743862:0.280915:0.563587:0.280916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x f x:@0.610691:0.297529:0.642787:0.297529:0.642787:0.281060:0.610691:0.281060:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.667986:0.297529:0.675461:0.297529:0.675461:0.281060:0.667986:0.281060:0.000000
:@0.679602:0.296894:0.694255:0.296894:0.694255:0.283521:0.679602:0.283521:0.000000
a b:@0.704252:0.297528:0.729394:0.297528:0.729394:0.281060:0.704252:0.281060:0.000000:0.000000:0.000000
En el cálculo diferencial se estudian problemas fundamentales. Por :@0.404235:0.329844:0.895863:0.329844:0.895863:0.313346:0.404235:0.313346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ejemplo, hallar la ecuación cartesiana o vectorial de la recta tangente :@0.404235:0.347195:0.895915:0.347195:0.895915:0.330697:0.404235:0.330697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a la gráfica de la función   en el punto   = ( ,  ( )), donde     ] ,  [. :@0.404235:0.364546:0.895905:0.364553:0.895905:0.348055:0.404235:0.348048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.578467:0.364661:0.582764:0.364661:0.582764:0.348193:0.578467:0.348193:0.000000
P:@0.672600:0.364661:0.681384:0.364661:0.681384:0.348193:0.672600:0.348193:0.000000
x f x:@0.706738:0.364661:0.743292:0.364668:0.743292:0.348199:0.706738:0.348193:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.714015:0.367829:0.718968:0.367829:0.718968:0.358211:0.714015:0.358211:0.000000
0:@0.743084:0.367829:0.748037:0.367829:0.748037:0.358211:0.743084:0.358211:0.000000
x:@0.816979:0.364668:0.824454:0.364668:0.824454:0.348199:0.816979:0.348199:0.000000
0:@0.824249:0.367829:0.829202:0.367829:0.829202:0.358211:0.824249:0.358211:0.000000
:@0.833687:0.364034:0.848340:0.364034:0.848340:0.350661:0.833687:0.350661:0.000000
a b:@0.858395:0.364668:0.883575:0.364668:0.883575:0.348199:0.858395:0.348199:0.000000:0.000000:0.000000
Originalmente, el concepto de derivada se introdujo para resolver :@0.404236:0.381903:0.895914:0.381903:0.895914:0.365406:0.404236:0.365406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
problemas relativos a tangentes de curvas. Más adelante, se aplicó al :@0.404236:0.399254:0.895957:0.399254:0.895957:0.382756:0.404236:0.382756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cálculo de velocidades y también se aplicó al estudio de variación de :@0.404236:0.416605:0.895970:0.416605:0.895970:0.400107:0.404236:0.400107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función, la razón de crecimiento. Este problema ya fue tratado con :@0.404236:0.433956:0.895953:0.433956:0.895953:0.417458:0.404236:0.417458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones cuadráticas en el primer curso de bachillerato (libro 1).:@0.404236:0.451306:0.851223:0.451306:0.851223:0.434809:0.404236:0.434809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean   ≠ 0,   = ( ,  ( )),   = (  +  ,   (  +  ))    ( ).:@0.404236:0.483738:0.792658:0.483745:0.792658:0.467247:0.404236:0.467240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.442035:0.483853:0.451436:0.483853:0.451436:0.467385:0.442035:0.467385:0.000000
P:@0.485921:0.483853:0.494706:0.483853:0.494706:0.467385:0.485921:0.467385:0.000000
0:@0.494704:0.487021:0.499657:0.487021:0.499657:0.477403:0.494704:0.477403:0.000000
x f x:@0.524703:0.483860:0.561751:0.483860:0.561751:0.467392:0.524703:0.467392:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.532176:0.487021:0.537129:0.487021:0.537129:0.477403:0.532176:0.477403:0.000000
0:@0.561749:0.487021:0.566702:0.487021:0.566702:0.477403:0.561749:0.477403:0.000000
P:@0.585505:0.483860:0.594290:0.483860:0.594290:0.467392:0.585505:0.467392:0.000000
1:@0.594290:0.487021:0.599244:0.487021:0.599244:0.477403:0.594290:0.477403:0.000000
x:@0.624287:0.483860:0.631762:0.483860:0.631762:0.467392:0.624287:0.467392:0.000000
0:@0.631762:0.487021:0.636715:0.487021:0.636715:0.477403:0.631762:0.477403:0.000000
h f x:@0.655806:0.483860:0.693971:0.483860:0.693971:0.467392:0.655806:0.467392:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.693969:0.487021:0.698922:0.487021:0.698922:0.477403:0.693969:0.477403:0.000000
h:@0.718014:0.483860:0.727416:0.483860:0.727416:0.467392:0.718014:0.467392:0.000000
:@0.743464:0.483226:0.758116:0.483226:0.758116:0.469853:0.743464:0.469853:0.000000
G f:@0.762258:0.483860:0.783950:0.483860:0.783950:0.467392:0.762258:0.467392:0.000000:0.000000:0.000000
La pendiente  ( ) de la recta   que pasa por los puntos   y   está :@0.404232:0.518446:0.895910:0.518446:0.895910:0.501949:0.404232:0.501949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m h:@0.501714:0.518562:0.531864:0.518562:0.531864:0.502093:0.501714:0.502093:0.000000:0.000000:0.000000
L:@0.620696:0.518562:0.628537:0.518562:0.628537:0.502093:0.620696:0.502093:0.000000
h:@0.628459:0.521790:0.633940:0.521790:0.633940:0.512189:0.628459:0.512189:0.000000
P:@0.814910:0.518562:0.823695:0.518562:0.823695:0.502093:0.814910:0.502093:0.000000
0:@0.823715:0.521723:0.828668:0.521723:0.828668:0.512105:0.823715:0.512105:0.000000
P:@0.845236:0.518562:0.854021:0.518562:0.854021:0.502093:0.845236:0.502093:0.000000
1:@0.854026:0.521723:0.858979:0.521723:0.858979:0.512105:0.854026:0.512105:0.000000
definida como::@0.404241:0.535797:0.510950:0.535797:0.510950:0.519299:0.404241:0.519299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m h:@0.543240:0.562054:0.573390:0.562054:0.573390:0.545586:0.543240:0.545586:0.000000:0.000000:0.000000
( ) =                           ,   ≠ 0,:@0.558036:0.561939:0.752769:0.561939:0.752769:0.545441:0.558036:0.545441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.713025:0.562054:0.722426:0.562054:0.722426:0.545586:0.713025:0.545586:0.000000
 :@0.404241:0.579289:0.408383:0.579289:0.408383:0.562792:0.404241:0.562792:0.000000
con lo que la ecuación cartesiana de la recta   se escribe como sigue: :@0.404241:0.596640:0.895944:0.596647:0.895944:0.580149:0.404241:0.580143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.718434:0.596756:0.726275:0.596756:0.726275:0.580287:0.718434:0.580287:0.000000
h:@0.726117:0.599991:0.731598:0.599991:0.731598:0.590389:0.726117:0.590389:0.000000
y f x:@0.566187:0.621241:0.610381:0.621241:0.610381:0.604772:0.566187:0.604772:0.000000:0.000000:0.000000:0.000000:0.000000
 –  ( ) =  ( )(  –  ).:@0.573873:0.621126:0.729824:0.621125:0.729824:0.604627:0.573873:0.604628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.610378:0.624402:0.615331:0.624402:0.615331:0.614783:0.610378:0.614783:0.000000
m h x x:@0.640375:0.621241:0.716164:0.621241:0.716164:0.604772:0.640375:0.604772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.716162:0.624402:0.721116:0.624402:0.721116:0.614783:0.716162:0.614783:0.000000
 :@0.404241:0.638476:0.408383:0.638476:0.408383:0.621978:0.404241:0.621978:0.000000
El cociente  ( ) =                             con   ≠ 0 se llama cociente:@0.404241:0.655826:0.850192:0.655826:0.850192:0.639329:0.404241:0.639329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m h:@0.485271:0.655942:0.515421:0.655942:0.515421:0.639473:0.485271:0.639473:0.000000:0.000000:0.000000
h:@0.687535:0.655942:0.696936:0.655942:0.696936:0.639473:0.687535:0.639473:0.000000
incremental; también es conocido como tasa de variación de la :@0.404241:0.680305:0.857684:0.680305:0.857684:0.663808:0.404241:0.663808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función   en el punto  . Por su parte, la tangente de la medida  ( ) :@0.404241:0.697656:0.884175:0.697656:0.884175:0.681158:0.404241:0.681159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.463366:0.697772:0.467662:0.697772:0.467662:0.681303:0.463366:0.681303:0.000000
x:@0.557747:0.697772:0.565222:0.697772:0.565222:0.681303:0.557747:0.681303:0.000000
0:@0.565215:0.700933:0.570168:0.700933:0.570168:0.691315:0.565215:0.691315:0.000000
θ:@0.849104:0.704730:0.858726:0.704730:0.858726:0.686594:0.849104:0.686594:0.000000
h:@0.864678:0.697771:0.874080:0.697771:0.874080:0.681302:0.864678:0.681302:0.000000
del ángulo que forma la recta   y la recta que pasa por   y:@0.404239:0.715006:0.823992:0.715006:0.823992:0.698509:0.404239:0.698509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.616232:0.715122:0.624073:0.715122:0.624073:0.698653:0.616232:0.698653:0.000000
h:@0.623972:0.718352:0.629453:0.718352:0.629453:0.708751:0.623972:0.708751:0.000000
P:@0.798291:0.715122:0.807076:0.715122:0.807076:0.698653:0.798291:0.698653:0.000000
0:@0.807076:0.718284:0.812029:0.718284:0.812029:0.708666:0.807076:0.708666:0.000000
R = (  +  ,   ( )) está definida como::@0.404240:0.741264:0.665084:0.741268:0.665084:0.724770:0.404240:0.724766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.439072:0.741379:0.446547:0.741379:0.446547:0.724911:0.439072:0.724911:0.000000
0:@0.446541:0.744544:0.451494:0.744544:0.451494:0.734926:0.446541:0.734926:0.000000
h f x:@0.470587:0.741383:0.508751:0.741383:0.508751:0.724914:0.470587:0.724914:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.508749:0.744544:0.513703:0.744544:0.513703:0.734926:0.508749:0.734926:0.000000
tan( ( )) =                          ,   ≠ 0.:@0.531331:0.772875:0.764687:0.772874:0.764687:0.756376:0.531331:0.756377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
θ:@0.560122:0.779948:0.569744:0.779948:0.569744:0.761812:0.560122:0.761812:0.000000
h:@0.575254:0.772989:0.584655:0.772989:0.584655:0.756521:0.575254:0.756521:0.000000
h:@0.724943:0.772989:0.734345:0.772989:0.734345:0.756521:0.724943:0.756521:0.000000
 :@0.404236:0.790224:0.408378:0.790224:0.408378:0.773727:0.404236:0.773727:0.000000
Para   > 0 se tiene   +   >  . Nota que para   > 0 cada vez más pe-:@0.404236:0.807575:0.891692:0.807575:0.891692:0.791077:0.404236:0.791077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.438914:0.807691:0.448315:0.807691:0.448315:0.791222:0.438914:0.791222:0.000000
x:@0.539420:0.807691:0.546895:0.807691:0.546895:0.791222:0.539420:0.791222:0.000000
0:@0.546943:0.810853:0.551896:0.810853:0.551896:0.801235:0.546943:0.801235:0.000000
h:@0.571374:0.807691:0.580775:0.807691:0.580775:0.791222:0.571374:0.791222:0.000000
x:@0.600253:0.807691:0.607728:0.807691:0.607728:0.791222:0.600253:0.791222:0.000000
0:@0.607759:0.810853:0.612713:0.810853:0.612713:0.801235:0.607759:0.801235:0.000000
h:@0.727552:0.807691:0.736953:0.807691:0.736953:0.791222:0.727552:0.791222:0.000000
queño, la recta   se acerca cada vez más a la recta  , lo que implica :@0.404242:0.824926:0.895845:0.824926:0.895845:0.808428:0.404242:0.808428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.515248:0.825042:0.523089:0.825042:0.523089:0.808573:0.515248:0.808573:0.000000
h:@0.523002:0.828271:0.528483:0.828271:0.528483:0.818670:0.523002:0.818670:0.000000
L:@0.773705:0.825042:0.781546:0.825042:0.781546:0.808573:0.773705:0.808573:0.000000
que la pendiente  ( ) se aproxima cada vez más a la pendiente   de :@0.404242:0.842277:0.895945:0.842277:0.895945:0.825779:0.404242:0.825779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m h:@0.526632:0.842392:0.556783:0.842392:0.556783:0.825924:0.526632:0.825924:0.000000:0.000000:0.000000
m:@0.855411:0.842392:0.870207:0.842392:0.870207:0.825924:0.855411:0.825924:0.000000
L:@0.404242:0.859743:0.412083:0.859743:0.412083:0.843274:0.404242:0.843274:0.000000
, y esto, a su vez, significa que  ( ) se aproxima a   conforme     0 . :@0.412083:0.859627:0.895912:0.859629:0.895912:0.843131:0.412083:0.843130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
θ:@0.619004:0.866703:0.628625:0.866703:0.628625:0.848567:0.619004:0.848567:0.000000
h:@0.634576:0.859744:0.643977:0.859744:0.643977:0.843276:0.634576:0.843276:0.000000
θ:@0.754135:0.866703:0.763757:0.866703:0.763757:0.848567:0.754135:0.848567:0.000000
h:@0.841085:0.859744:0.850487:0.859744:0.850487:0.843276:0.841085:0.843276:0.000000
→:@0.854282:0.867728:0.870426:0.867728:0.870426:0.847865:0.854282:0.847865:0.000000
+:@0.882715:0.853276:0.889016:0.853276:0.889016:0.843658:0.882715:0.843658:0.000000
En la Figura 6.1., se muestran: una porción de la gráfica de la función  , :@0.404244:0.876979:0.895885:0.876979:0.895885:0.860482:0.404244:0.860482:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.884692:0.877095:0.888988:0.877095:0.888988:0.860626:0.884692:0.860626:0.000000
una porción de la recta   que pasa por   y  , el triángulo rectángulo :@0.404244:0.894330:0.895912:0.894329:0.895912:0.877831:0.404244:0.877832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.571543:0.894446:0.579384:0.894446:0.579384:0.877977:0.571543:0.877977:0.000000
h:@0.579289:0.897674:0.584770:0.897674:0.584770:0.888073:0.579289:0.888073:0.000000
P:@0.684562:0.894445:0.693347:0.894445:0.693347:0.877976:0.684562:0.877976:0.000000
0:@0.692190:0.897607:0.697143:0.897607:0.697143:0.887989:0.692190:0.887989:0.000000
P:@0.712613:0.894445:0.721398:0.894445:0.721398:0.877976:0.712613:0.877976:0.000000
1:@0.720242:0.897607:0.725195:0.897607:0.725195:0.887989:0.720242:0.887989:0.000000
P RP:@0.404236:0.911795:0.436160:0.911795:0.436160:0.895327:0.404236:0.895327:0.000000:0.000000:0.000000:0.000000
0:@0.413021:0.914958:0.417974:0.914958:0.417974:0.905339:0.413021:0.905339:0.000000
1:@0.436160:0.914958:0.441113:0.914958:0.441113:0.905339:0.436160:0.905339:0.000000
, y la recta tangente   a la gráfica de   en el punto   = ( ,   ( )).:@0.441113:0.911680:0.890050:0.911680:0.890050:0.895182:0.441113:0.895182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.583328:0.911795:0.591168:0.911795:0.591168:0.895327:0.583328:0.895327:0.000000
f:@0.696085:0.911795:0.700381:0.911795:0.700381:0.895327:0.696085:0.895327:0.000000
P:@0.790468:0.911795:0.799253:0.911795:0.799253:0.895327:0.790468:0.895327:0.000000
0:@0.799249:0.914958:0.804203:0.914958:0.804203:0.905339:0.799249:0.905339:0.000000
x f x:@0.829248:0.911795:0.870438:0.911795:0.870438:0.895327:0.829248:0.895327:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.836721:0.914958:0.841674:0.914958:0.841674:0.905339:0.836721:0.905339:0.000000
0:@0.870437:0.914958:0.875390:0.914958:0.875390:0.905339:0.870437:0.905339:0.000000
Saberes previos:@0.199646:0.115710:0.307805:0.115710:0.307805:0.100238:0.199646:0.100238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es la derivada de :@0.199884:0.144338:0.348219:0.144338:0.348219:0.129274:0.199884:0.129274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una función?:@0.153341:0.160180:0.237138:0.160180:0.237138:0.145116:0.153341:0.145116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.207711:0.363493:0.207711:0.363493:0.192238:0.199646:0.192238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué relación hay entre :@0.199884:0.236338:0.356400:0.236338:0.356400:0.221275:0.199884:0.221275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
derivar e integrar?:@0.153341:0.252180:0.267746:0.252180:0.267746:0.237117:0.153341:0.237117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.199644:0.331889:0.346429:0.331889:0.346429:0.316417:0.199644:0.316417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática e Historia:@0.199880:0.360939:0.355549:0.360939:0.355549:0.345467:0.199880:0.345467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El cálculo diferencial surgió  de :@0.153337:0.376359:0.354477:0.376359:0.354477:0.361295:0.153337:0.361295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las ideas del matemático francés. :@0.153337:0.392201:0.365227:0.392201:0.365227:0.377137:0.153337:0.377137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pierre Fermat, quien trató de :@0.153337:0.408043:0.342252:0.408043:0.342252:0.392979:0.153337:0.392979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolver el problema del cálculo :@0.153337:0.423885:0.361848:0.423885:0.361848:0.408821:0.153337:0.408821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los valores extremos (máxi-:@0.153337:0.439727:0.350025:0.439727:0.350025:0.424663:0.153337:0.424663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mos y mínimos) de una fun-:@0.153337:0.455569:0.338224:0.455569:0.338224:0.440505:0.153337:0.440505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción. Los esfuerzos realizados :@0.153337:0.471411:0.344185:0.471411:0.344185:0.456347:0.153337:0.456347:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por Isaac Newton (1642-1727) :@0.153337:0.487253:0.354583:0.487253:0.354583:0.472189:0.153337:0.472189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y Gottfried Leibniz (1646-1716) :@0.153337:0.503095:0.359543:0.503095:0.359543:0.488031:0.153337:0.488031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son los que permitieron ligar los :@0.153337:0.518937:0.364256:0.518937:0.364256:0.503873:0.153337:0.503873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
problemas del cálculo del área :@0.153337:0.534779:0.352787:0.534779:0.352787:0.519715:0.153337:0.519715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bajo una curva y de la tangente :@0.153337:0.550621:0.360511:0.550621:0.360511:0.535557:0.153337:0.535557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a la gráfica de una curva en un :@0.153337:0.566463:0.354690:0.566463:0.354690:0.551399:0.153337:0.551399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
punto dado de esta, dando :@0.153337:0.582304:0.334018:0.582304:0.334018:0.567241:0.153337:0.567241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lugar así al cálculo diferencial e :@0.153337:0.598146:0.354848:0.598146:0.354848:0.583083:0.153337:0.583083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
integral.:@0.153337:0.613988:0.204313:0.613988:0.204313:0.598925:0.153337:0.598925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga escribe:@0.153337:0.638332:0.261006:0.638332:0.261006:0.623071:0.153337:0.623071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.198737:0.638134:0.213442:0.638134:0.213442:0.623071:0.198737:0.623071:0.000000:0.000000:0.000000
 acerca de las :@0.261006:0.638134:0.349904:0.638134:0.349904:0.623071:0.261006:0.623071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicaciones del calculo diferen-:@0.153337:0.653976:0.359207:0.653976:0.359207:0.638913:0.153337:0.638913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cial e integral.:@0.153337:0.669818:0.240425:0.669818:0.240425:0.654755:0.153337:0.654755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.602395:0.555858:0.620119:0.555858:0.620119:0.539390:0.602395:0.539390:0.000000:0.000000:0.000000
( +  ) –  ( ):@0.606691:0.555743:0.702788:0.555743:0.702788:0.539245:0.606691:0.539245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.620119:0.556506:0.625072:0.556506:0.625072:0.546888:0.620119:0.546888:0.000000
h:@0.640021:0.555858:0.649423:0.555858:0.649423:0.539390:0.640021:0.539390:0.000000
f x:@0.674159:0.555858:0.691883:0.555858:0.691883:0.539390:0.674159:0.539390:0.000000:0.000000:0.000000
0:@0.691882:0.556506:0.696835:0.556506:0.696835:0.546888:0.691882:0.546888:0.000000
h:@0.647882:0.572197:0.657284:0.572197:0.657284:0.555728:0.647882:0.555728:0.000000
f x:@0.544559:0.649414:0.562283:0.649414:0.562283:0.632945:0.544559:0.632945:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.548855:0.649299:0.648132:0.649299:0.648132:0.632801:0.548855:0.632801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.562283:0.650061:0.567236:0.650061:0.567236:0.640442:0.562283:0.640442:0.000000
h:@0.585366:0.649414:0.594767:0.649414:0.594767:0.632945:0.585366:0.632945:0.000000
f x:@0.619504:0.649414:0.637228:0.649414:0.637228:0.632945:0.619504:0.632945:0.000000:0.000000:0.000000
0:@0.637225:0.650061:0.642178:0.650061:0.642178:0.640442:0.637225:0.640442:0.000000
h:@0.591646:0.665753:0.601048:0.665753:0.601048:0.649284:0.591646:0.649284:0.000000
f x:@0.616727:0.765927:0.634451:0.765927:0.634451:0.749458:0.616727:0.749458:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.621023:0.765811:0.715867:0.765811:0.715867:0.749314:0.621023:0.749314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.634449:0.766575:0.639402:0.766575:0.639402:0.756957:0.634449:0.756957:0.000000
h:@0.655798:0.765927:0.665199:0.765927:0.665199:0.749458:0.655798:0.749458:0.000000
f x:@0.687239:0.765927:0.704963:0.765927:0.704963:0.749458:0.687239:0.749458:0.000000:0.000000:0.000000
0:@0.704962:0.766575:0.709915:0.766575:0.709915:0.756957:0.704962:0.756957:0.000000
h:@0.661597:0.782266:0.670998:0.782266:0.670998:0.765797:0.661597:0.765797:0.000000
p:@0.144242:0.902755:0.155723:0.902755:0.155723:0.892730:0.144242:0.892730:0.000000
 :@0.155723:0.903463:0.158604:0.903463:0.158604:0.891986:0.155723:0.891986:0.000000
Figura 6.1.:@0.158604:0.903463:0.207173:0.903463:0.207173:0.891986:0.158604:0.891986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.304007:0.859062:0.309461:0.859062:0.309461:0.847606:0.304007:0.847606:0.000000
P:@0.157577:0.884520:0.163689:0.884520:0.163689:0.873064:0.157577:0.873064:0.000000
0:@0.163690:0.885463:0.167136:0.885463:0.167136:0.878773:0.163690:0.878773:0.000000
 = ( ,  ( )):@0.167136:0.884441:0.222059:0.884441:0.222059:0.872964:0.167136:0.872964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x f x:@0.184559:0.884521:0.210332:0.884521:0.210332:0.873065:0.184559:0.873065:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.189759:0.885463:0.193204:0.885463:0.193204:0.878773:0.189759:0.878773:0.000000
0:@0.210331:0.885463:0.213776:0.885463:0.213776:0.878773:0.210331:0.878773:0.000000
P:@0.273670:0.828757:0.279781:0.828757:0.279781:0.817301:0.273670:0.817301:0.000000
1:@0.279784:0.829703:0.283230:0.829703:0.283230:0.823013:0.279784:0.823013:0.000000
 = (  +  ,  ( + )):@0.283229:0.828681:0.373397:0.828681:0.373397:0.817204:0.283229:0.817204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.300289:0.828761:0.305489:0.828761:0.305489:0.817305:0.300289:0.817305:0.000000
0:@0.305491:0.829703:0.308936:0.829703:0.308936:0.823013:0.305491:0.823013:0.000000
h f x h:@0.321855:0.828761:0.365114:0.828761:0.365114:0.817305:0.321855:0.817305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.346013:0.829703:0.349459:0.829703:0.349459:0.823013:0.346013:0.823013:0.000000
R:@0.266972:0.884525:0.273633:0.884525:0.273633:0.873069:0.266972:0.873069:0.000000
 = (  +  ,  ( )):@0.273633:0.884445:0.349045:0.884441:0.349045:0.872964:0.273633:0.872968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.291055:0.884525:0.296255:0.884525:0.296255:0.873069:0.291055:0.873069:0.000000
0:@0.296254:0.885463:0.299699:0.885463:0.299699:0.878773:0.296254:0.878773:0.000000
h f x:@0.312981:0.884521:0.337319:0.884521:0.337319:0.873065:0.312981:0.873065:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.337317:0.885463:0.340763:0.885463:0.340763:0.878773:0.337317:0.878773:0.000000
θ:@0.246991:0.858665:0.252948:0.858665:0.252948:0.847439:0.246991:0.847439:0.000000
( ):@0.252947:0.854248:0.265917:0.854248:0.265917:0.844206:0.252947:0.844206:0.000000:0.000000:0.000000
h:@0.256570:0.854318:0.262293:0.854318:0.262293:0.844294:0.256570:0.844294:0.000000
θ:@0.227756:0.876412:0.233713:0.876412:0.233713:0.865185:0.227756:0.865185:0.000000