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UBA - CienciaS :: Ver Tema - Enunciados Final 23/12/08
UBA - CienciaS
http://ubacs.com.ar/ubacs/

Enunciados Final 23/12/08
http://ubacs.com.ar/ubacs/viewtopic.php?f=62&t=802
Página 1 de 1

Autor:  Diana [ 26 Dic 2008, 22:30 ]
Asunto:  Enunciados Final 23/12/08

Es una aproximación de los enunciados que me pasaron, para que vean una idea de lo que toman:

1)
a) Demostrar que en una region D el area de esa region es equivalente a la circulacion de sobre la frontera de D.
b) Calcular el area de la region dada entre el eje y la curva parametrizada por con .

2)
a) Si entonces demostrar que
b) Sea (no la sé), mostrar que
c) F como en el item anterior demostrar que no se cumple .

3)
a) Demostrar para una de que las soluciones forman un espacio vectorial de dim=2.
b) Hallar en forma explícita una base de soluciones si

4) Sea
a) Hallar todas las soluciones y el intervalo maximal. sugerencia: hallar el cambio de variable necesario
b) Hallar las soluciones de x tal que

Autor:  Pato [ 27 Dic 2008, 12:07 ]
Asunto:  Re: Enunciados Final 23/12/08

En el ejercicio 2, sabes si la F tenia algun "problema", o sea, no estaba definida en algún lado (en un abierto conexo, jaa)?

Autor:  Quimey [ 27 Dic 2008, 12:53 ]
Asunto:  Re: Enunciados Final 23/12/08

Seguro que que es el contraejemplo estandar (o parecida)

Autor:  ALE [ 02 Feb 2009, 15:38 ]
Asunto:  Re: Enunciados Final 23/12/08

El ejercicio 4 lo tomaron en el recuperatorio del 2do parcial...

no parece muy dificil! :)

Alguno se presento? para saber sobre las correcciones, si son muy detallistas o no tanto...

Autor:  bel [ 02 Feb 2009, 21:44 ]
Asunto:  Re: Enunciados Final 23/12/08

che, es bastante práctico!
alguién tiene el del 29???

alguien lo rinde ahora???

Autor:  nahuelv [ 30 Sep 2010, 19:46 ]
Asunto:  Re: Enunciados Final 23/12/08

Alguien me pasa un tip para la ecuación diferencial última, onda como empiezo!

Autor:  ivoo [ 02 Oct 2010, 15:31 ]
Asunto:  Re: Enunciados Final 23/12/08


Autor:  Landroval [ 24 Ago 2011, 17:09 ]
Asunto:  Re: Enunciados Final 23/12/08

Alguien sabe como se resuelve el 4? Yo no lo puedo sacar :S.

Autor:  Maxtwo [ 24 Ago 2011, 19:34 ]
Asunto:  Re: Enunciados Final 23/12/08

El cambio de variable seguro es t=e^y, reemplazas todas las x( t) con lo apropiado usando regla de la cadena y creo que sale.

Autor:  KillSchrodingerCat [ 28 Jul 2012, 20:02 ]
Asunto:  Re: Enunciados Final 23/12/08

Dejo la respuesta del 4.

Efectivamente sale con el cambio de variable que mencionan arriba (de hecho esta en la practica).

La solucion general es:



El intervalo maximal es

Y para que se cumpla el limite hay que pedir


Cualquier duda o correccion no duden en postear.

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