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Cálculo: Límites y continuidad

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Cálculo: Límites y continuidad

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Cuestionario rápido sobre límites y continuidad

Created by

Mario Escobar
Mario Escobar
Ecuador

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Cálculo: Límites y continuidad
 

Cálculo: Límites y continuidadOnline version

Cuestionario rápido sobre límites y continuidad

by Mario Escobar
1

1) ¿Cuál es el valor del límite de 3x^2 - 4x + 1 cuando x→2?

2

2) ¿Cuál es el valor del límite de (x^2 - 1)/(x - 1) cuando x→1?

3

3) ¿La función es continua en x=1 si f(x)= x^2 para x≠1 y f(1)=2?

4

4) ¿En qué valor de x ocurre el mínimo de f(x)=x^2 - 4x + 3?

5

5) ¿En qué punto ocurre el máximo de f(x)=-x^2 + 6x?

Explicación

Al sustituir x=2 obtenemos 12-8+1=5.

Factor( x^2-1 )=(x-1)(x+1); al simplificar queda x+1→2.

La función no coincide en x=1 (lim=2 y f(1)=2) pero en este caso sí coincide; si f(1)≠lim, no es continua.

Completar el cuadrado o derivar: x^2-4x+3=(x-2)^2-1; mínimo en x=2.

Parábola hacia abajo; vértice en x=3 da y=9.

 
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