1000410_5_TRACOL3 (2)
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Trabajo colaborativo 3
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Unidad 3 Cálculo Diferencial
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Escuela de Ciencias B
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á
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sicas, tecnolog
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í
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a e Ingenier
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í
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a
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Universidad Nacional Abierta y Distancia UNAD
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Presentado a !utor" Cristian David Ca#ac$o
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%ru&o '(()'(*+
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$aron aray Cano -ora C.D '(/0+()0/ 1 Angela Adriana Da2a ate C.D"+/4'355)
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-ayo /('+"
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Co&yrig$t 6 /('+ &or $aron aray Cano -ora 1 Angela Adriana Da2a ate
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Abstract
En este docu#ento encontrare#os una serie de e7ercicios resueltos, &ara evidenciar, laa&ro&iaci8n de conce&tos corres&ondientes, a la unidad 3 9Analisis de las derivadas y susa&licaciones:, del curso Calculo Diferencial"
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Contenido
Introducci8n """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" +
.b7etivos """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 0 E7ercicio ' """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 5 E7ercicio / """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 5 E7ercicio 3 """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" ; E7ercicio ) """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 4 E7ercicio + """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" '( E7ercicio 0 """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" '(
E7ercicio 5 """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" '/ E7ercicio ; """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" ') E7ercicio 4 """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" ') E7ercicio '( """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" '+ Conclusiones """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" '5 <ista de referencias """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" ';
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Introducción
En esta actividad a&licare#os el conoci#iento ad=uirido durante el curso de cálculo diferencial,llevándolo al desarrollo de e7ercicios &rácticos, y situaciones cotidianas, &ara de esta #anera darsoluci8n a los e7ercicios &ro&uestos<os e7ercicios desarrollados a lo largo de este traba7o, a&lican los conce&tos generales del calculointegral , &artiendo del estudio de las &ro&iedades de los i#ites, el lí#ite de las funciones, yasíntotas y la continuidad de los li#ites"
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Objetivos
General
Evidenciar la a&ro&iaci8n de los conce&tos corres&ondientes a la unidad 3, del curso de cálculoDiferencial"
Específicos
A&licar el cálculo diferencial en la soluci8n de los e7ercicios &ro&uestos
Desarrollar los e7ercicios &ro&uestos, a trav>s de la a&licaci8n de lí#ites y derivadas" ?ortalecer los conce&tos de la unidad 3" ?ortalecer en los estudiantes los conoci#ientos del curso a trav>s de e7ercicios &rácticos, =uere=uieran la soluci8n a trav>s del cálculo diferencial Desarrollar en los estudiantes del curso análisis crítico en el &lantea#iento y soluci8n de#odelos #ate#áticos basados en los lí#ites y la continuidad a trav>s de los &roble#as &lanteados en el traba7o colaborativo"
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@allar la ecuaci8n de la recta tangente a la curva
Ejercicio 1
/,':"/3'9:///9':/(y&arafy
Ejercicio 2
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)),)3,3)/3,3;3,3;,/:"'9:ln),,9':9(":9)"':9:)9:)9:)9:)9':9:)9':9':9':));sif$allarfffff
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Ejercicio 3
3"
egla de la cadena ( )
egla de &otencia
i#&lifica#os
egla de la cadena
egla de derivaci8n
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egla de derivaci8n
i#&lificar
ustituir en la ecuaci8n
ustituir en la ecuaci8n
i#&lificar
Ejercicio 4
)"
( )
acar la constante ( )
egla de cociente
A&licar regla de &otencias
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i#&lificar
Ejercicio 5
+"
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( )
egla de derivaci8n
egla de derivaci8n
i#&lificar
Derivadas de orden su&erior
Ejercicio
! @allar la tercera derivada de
( )
acar la constante
egla de la cadena
egla de derivaci8n
Constante
i#&lificar
ustituir en la ecuaci8n u/
i#&lificar
Constante
egla de la cadena
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egla de derivaci8n
egla de derivaci8n
/"'i#&lificar
ustituir en la ecuaci8n u/
i#&lificar
Ejercicio "
"! @allar la segunda derivada de
!o#a#os I co#o constante
A&lica#os la regla del &roducto ( )
esolve#os
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A&lica#os regla de derivaci8n
esolve#os
A&lica#os regla de derivaci8n
A&lica#os regla de derivaci8n
i#&lifica#os ( )
!o#a#os
!ratar I co#o constante( )
A&lica#os la regla del &roducto ( )
!o#a#os
A&lica#os la regla de derivaci8n
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!o#a#os
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A&lica#os la regla de la su#aFdiferencia
A&lica#os la regla de derivaci8n
Derivada de una constante
Ejercicio #
Usando <G$os&ital $allar el lí#ite de
Este lí#ite no tiene soluci8n
Ejercicio $
De la curva $allar
a" <as coordenadas del &unto critico b" <os de inflei8n si los $ay
( )
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%rafica
Ejercicio 1%
En <a construcci8n de una obra se debe $acer un &edido de ce#ento" Hu> Cantidad de bultos 9:debo solicitar a la fabrica, tal =ue el costo de este &edido sea #ini#oJ
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&onclusiones
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En el &resente traba7o &ode#os concluir El caculo integral, nos &resenta $erra#ientas =ue nos ayudana resolver diferentes situaciones, a trav>s de la e7ecuci8n de sus conce&tos"
Al encontrar la soluci8n a estos &roble#as, ve#os co#o &or #edio del cálculo, no soloencontra#os la soluci8n &ara un &lantea#iento inicial, sino &ara otras situaciones, =ue surgen atrav>s del desarrollo de cada e7ercicio"
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'ista de referencias
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Unidad 3, -odulo Calculo Diferencial, Universidad Nacional Abierta a Distancia UNADBogotá"
%uía ubrica !raba7o Colaborativo 3, Escuela de Ciencias Básicas !ecnología e Ingeniería,Universidad Nacional Abierta a Distancia UNAD Bogotá"
yllabus Cálculo diferencial, Escuela de Ciencias Básicas !ecnología e Ingeniería, Universidad Nacional Abierta a Distancia UNAD Bogotá"