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Ejercicios breves de continuidad

Created by

Natali
Natali
Mexico

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Funciones continuas y límites
 

Funciones continuas y límitesOnline version

Ejercicios breves de continuidad

by Natali
1

Si f es continua en un intervalo I, entonces f tiene límite en cada punto de I.

2

Una función puede ser continua en un punto sin tener límite en ese punto.

3

Si lim_{x->a} f(x) = 0 y f(a) = 1, entonces f es continua en a.

4

La multiplicación de dos funciones continuas es continua.

5

Si f es continua en c, entonces lim_{x->c} f(x) = f(c).

6

La suma de dos funciones continuas es continua en todo punto donde ambas son continuas.

7

La derivada de una función continua siempre existe.

8

Toda función constante no es continua.

9

La composición de una función continua con una continua en su salida es continua: si f es continua en a y g es continua en f(a), entonces g∘f es continua en a.

10

La existencia de un límite en a siempre implica que f(a) = lim f(x).

 
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