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Trabajo Práctico 7: continuidad - AM I
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Trabajo Práctico 7: continuidad (definición y propiedades)
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TRABAJO PRÁCTICO 7CONTINUIDAD: DEFINICIÓN Y PROPIEDADES.
y y
f f
2 2
4 x 4 x
y y
f
f 3
3 2
2
4 x
4 x
1. Observar los gráficos de arriba y determinar si f es continua en . De no
ser continua, indicar cual condición no se está cumpliendo.
2. Repasar la definición de continuidad y contestar Verdadero o Falso a las
siguientes afirmaciones (justifique su elección):
a. Si f no está definida en , entonces no existe el
b. Si , entonces
c. Si , entonces
3. Dibujar una función cuyo dominio sea el intervalo y que sea continua
en el punto y discontinua en .
4. Indicar los puntos donde las siguientes funciones f A IR (A = Dom(f)) no
son continuas o no están definidas y construir, si es posible (en cada caso),
una nueva función que sea continua en esos puntos y que coincida con
en todos los donde ésta esté definida y sea continua. Indicar, en cada
caso, el conjunto
a.
b.
c.
d.
e. (grafique la función)
1
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