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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"