Certamen 2 - Matemáticas III (2007-2).pdf - A Departamento de Matem´ aticas UTFSM Certamen 2 MAT-023 Segundo Semestre 2007 Tiempo 100 minutos No se

Certamen 2 - Matemáticas III (2007-2).pdf - A...

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A Departamento de Matem´ aticas, UTFSM Certamen 2, MAT-023, Segundo Semestre 2007 Tiempo: 100 minutos. No se puede utilizar calculadora. 1.) Resolver el problema de valor inicial y + 4 y + 13 y = 13 u 5 ( t ) , y (0) = 0 , y (0) = 1 . Determinar el l´ ımite de la soluci´ on y ( t ) a medida que t tiende a infinito. 25 puntos 2.a) Sea f ( t ) una funci´ on peri´ odica de per´ ıodo 2 t.q. f ( t ) = 3 si 0 t < 1 0 si 1 t < 2 . Calcule la transformada de Laplace L [ f ]( s ) = 0 f ( t ) e - st dt . 15 puntos b) Calcular la convoluci´ on sen 3 t * sen 3 t . Sugerencia: Use la transformada de Laplace. 15 puntos 3.) Sea f ( x ) = - 1 si 0 < x < π/ 2 1 si π/ 2 < x < π peri´ odica de per´ ıodo 2 π . a) Encuentre los primeros 3 t´
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