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UBA - CienciaS • Ver Tema - 1r parcial 2do cuatro 2010
UBACS Q&A Foro WikiCS
Fecha actual 01 Mar 2024, 17:31

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 Asunto: 1r parcial 2do cuatro 2010
NotaPublicado: 30 Dic 2010, 00:32 
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Registrado: 08 Ago 2008, 21:57
Mensajes: 299
Ejercicio 1
a) Probar que si las cuádricas Q y Q' son de distinto tipo (i.e. sin centro, con centro y sin puntos singulares, con puntos sing) entonces no existe un isoafin tal que
b) Sean
Encontrar los a y b tales que exista uno isoafin f demodo que
Ejercicio 2
Sea una curva par por long de arco, con curvatura y torsión constantes. Denotamos con su triedro de Fernet. Sea ahra la curva . Calcular el triedro de fernet de dicha curva, su curvatura y su torsión.
Ejercicio 3
Sea c una curva en par por long de arco con curvatura verificando: para todo t, donde L es una función escalar y p un punto de R^3
a) Probar que c es una curva plana
b) Probar que c está incluida en una circunferencia, hallar el radio de la misma y L en términos de la curvatura de c.
Ejercicio 4
Sean curvas del plano par por long de arco tales que . Si además probar que en un entorno de 0 envuelve a
Ejercicio 5
Probar que es una dup regular de R^3. VErificar que con y es una parametrización.


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