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UBA - CienciaS Foro de Alumnos 2008-08-11T16:15:40-03:00 http://ubacs.com.ar/ubacs/feed.php?f=37&t=465 2008-08-11T16:15:40-03:00 2008-08-11T16:15:40-03:00 http://ubacs.com.ar/ubacs/viewtopic.php?t=465&p=2430#p2430 <![CDATA[Re: [No Resuelto] Final 17/06/08 ejercicio 1]]>
Sea y tal que existe , . Existen también las derivadas parciales de en . Si además son contínuas en es diferenciable en .

Demostración:

=

Sea , tal que si .

Sea ,

Luego, es derivable en , y


Como cumple las hipótesis del teorema de Lagrange , existe tal que .
Si llamamos tenemos .

Definiendo , tal que si , razonando de forma análoga concluimos que existe = , tal que .

Luego,
.

Como las derivadas parciales son contínuas en :
Dado , existe tal que

y .

Tomando ,




Luego, es diferenciable en


Bueno, esa es la Becker's demo. Espero que esté bien texeada, y sirva, Salud os.

Estadísticas: Publicado por Agustin — 11 Ago 2008, 16:15

]]> 2008-08-11T15:54:58-03:00 2008-08-11T15:54:58-03:00 http://ubacs.com.ar/ubacs/viewtopic.php?t=465&p=2428#p2428 <![CDATA[Re: [No Resuelto] Final 17/06/08 ejercicio 1]]> Estadísticas: Publicado por Matias — 11 Ago 2008, 15:54

]]> 2008-08-11T15:51:48-03:00 2008-08-11T15:51:48-03:00 http://ubacs.com.ar/ubacs/viewtopic.php?t=465&p=2427#p2427 <![CDATA[Re: [No Resuelto] Final 17/06/08 ejercicio 1]]> Estadísticas: Publicado por exequiel131719 — 11 Ago 2008, 15:51

]]> 2008-08-11T15:50:29-03:00 2008-08-11T15:50:29-03:00 http://ubacs.com.ar/ubacs/viewtopic.php?t=465&p=2426#p2426 <![CDATA[Re: [No Resuelto] Final 17/06/08 ejercicio 1]]> Estadísticas: Publicado por Agustin — 11 Ago 2008, 15:50

]]> 2008-08-11T15:41:36-03:00 2008-08-11T15:41:36-03:00 http://ubacs.com.ar/ubacs/viewtopic.php?t=465&p=2424#p2424 <![CDATA[Re: [No Resuelto] Final 17/06/08 ejercicio 1]]> Estadísticas: Publicado por Matias — 11 Ago 2008, 15:41

]]> 2008-08-11T15:36:05-03:00 2008-08-11T15:36:05-03:00 http://ubacs.com.ar/ubacs/viewtopic.php?t=465&p=2423#p2423 <![CDATA[Re: [No Resuelto] Final 17/06/08 ejercicio 1]]>
Creo que vos podés darle el toque final ahora, viendo que es continua en , con lo que . Lo mismo con la otra derivada. Luego, acotás primero con la desigualdad triangular, y bueno, el resto a cargo tuyo. No se si aclaré; pero la intención era ayudar(me contradigo en la misma oración...). Saludos.

Estadísticas: Publicado por exequiel131719 — 11 Ago 2008, 15:36

]]> 2008-08-11T14:57:42-03:00 2008-08-11T14:57:42-03:00 http://ubacs.com.ar/ubacs/viewtopic.php?t=465&p=2418#p2418 <![CDATA[[No Resuelto] Final 17/06/08 ejercicio 1]]>
Bueno, el problema que me surgió se reduce a dos posibilidades, o a esto le falta que f es continua en U y lo que hay que hacer es demostrar que si f es C1 entonces es diferenciable, o hay que probar primero que si sus derivadas parciales son continuas entonces f también lo es (lo cual tengo entendido que no es cierto) para poder usar Lagrange.. Sino, hay que hacer una demostración diferente que la de C1 implica diferenciable, y no se me ocurre qué hacer..

Estadísticas: Publicado por Matias — 11 Ago 2008, 14:57

]]>