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Continuidad y discontinuidad: quiz completo

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Continuidad y discontinuidad: quiz completo

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Repaso de conceptos

Created by

JOHANNA PAMELA SANTAMARIA PEREZ
JOHANNA PAMELA SANTAMARIA PEREZ
Ecuador

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Continuidad y discontinuidad: quiz completo
 

Continuidad y discontinuidad: quiz completoOnline version

Repaso de conceptos

by JOHANNA PAMELA SANTAMARIA PEREZ
1

¿Qué significa que una función sea continua en x=a?

2

Discontinuidad removible ocurre cuando...

3

La discontinuidad removible también sucede si...

4

¿Qué tipo de discontinuidad hay cuando el límite no existe por oscilación alrededor de a?

5

Si f y g son continuas y la composición es f∘g, ¿cuándo es continua?

6

¿Qué tipo de continuidad usamos en el extremo izquierdo de [a,b]?

7

Si lim x→a f(x) existe pero f(a) ≠ lim f(x), ¿qué discontinuidad es?

8

La función f(x)=1/x en x=0 tiene

9

Una función es continua en [a,b] si es continua en…

10

Ejercicio: f(x)=|x| es continua en x=0. ¿Qué opción es correcta?

Explicación

La continuidad en a implica definición y coincidencia del límite con f(a).

Si el límite existe y f(a) no está definida, puede redefinirse para ser continua.

Si el límite existe pero el valor en a no coincide, hay una discontinuidad removible.

La oscilación alrededor de a impide un límite definido, creando discontinuidad oscilatoria.

La continuidad de la composición depende de la continuidad de g en x y de f en g(x).

En extremos, se evalúan límites laterales adecuados.

Existencia del límite y diferencia con f(a) indica salto; si se ajusta f(a) puede ser removible.

1/x no está definida en 0 y presenta asintota vertical.

Se verifica en el interior y se consideran los límites en los bordes.

La función valorada por norma absoluta es continua en todo punto, incluido 0.

 
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