Identify the values of x x in the interval [ − 6 , 10 ] \left\lbrack-6,10\right\rbrack where f f fails to be continuous. Explain your answers.

x = − 4 x=-4 x = − 4 ; The limit of f ( x ) f\left(x\right) f ( x ) as x → − 4 x\rightarrow-4 x → − 4 does not exist. x = 0 x=0 x = 0 ; The limit of f ( x ) f\left(x\right) f ( x ) as x → 0 x\rightarrow0 x → 0 is not equal to f ( 0 ) f\left(0\right) f ( 0 ) . x = 4 x=4 ; f ( 4 ) f\left(4\right) is undefined.

x = − 4 x=-4 x = − 4 ; The limit of f ( x ) f\left(x\right) f ( x ) as x → − 4 x\rightarrow-4 x → − 4 is not equal to f ( − 4 ) f\left(-4\right) . x = 0 x=0 x = 0 ; The limit of f ( x ) f\left(x\right) f ( x ) as x → 0 x\rightarrow0 x → 0 is not equal to f ( 0 ) f\left(0\right) f ( 0 ) .

x = − 4 x=-4 x = − 4 ; f ( − 4 ) f\left(-4\right) is undefined. x = 0 x=0 x = 0 ; The limit of f ( x ) f\left(x\right) f ( x ) as x → 0 x\rightarrow0 x → 0 does not exist. x = 4 x=4 ; The limit of f ( x ) f\left(x\right) f ( x ) as x → 4 x\rightarrow4 does not exist.

x = 0 x=0 x = 0 ; f ( 0 ) f\left(0\right) is undefined. x = 4 x=4 x = 4 ; The limit of f ( x ) f\left(x\right) f ( x ) as x → 4 x\rightarrow4 x → 4 does not exist.

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1. Limits and Continuity

Continuity

1. Limits and Continuity

Continuity: Study with Video Lessons, Practice Problems & Examples

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28PRACTICE PROBLEM

Identify the values of $x$ in the interval $open bracket negative 6 comma 10 close bracket$ where $f$ fails to be continuous. Explain your answers.

ANSWERS OPTIONS

$x=-4$ ; The limit of $f\left(x\right)$ as $x\rightarrow-4$ is not equal to $f of negative 4$ .

$x=0$ ; The limit of $f\left(x\right)$ as $x\rightarrow0$ is not equal to $f\left(0\right)$ .

$x=-4$ ; The limit of $f\left(x\right)$ as $x\rightarrow-4$ does not exist.

$x=0$ ; The limit of $f\left(x\right)$ as $x\rightarrow0$ is not equal to $f\left(0\right)$ .

$x equals 4$ ; $f of 4$ is undefined.

$x=-4$ ; $f of negative 4$ is undefined.

$x=0$ ; The limit of $f\left(x\right)$ as $x\rightarrow0$ does not exist.

$x equals 4$ ; The limit of $f\left(x\right)$ as $x right arrow 4$ does not exist.

$x=0$ ; $f of 0$ is undefined.

$x=4$ ; The limit of $f\left(x\right)$ as $x\rightarrow4$ does not exist.

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Continuity: Study with Video Lessons, Practice Problems & Examples

Identify the values of xx in the interval [−6,10]\left\lbrack-6,10\right\rbrack where ff fails to be continuous. Explain your answers.

Identify the values of $x$ in the interval $open bracket negative 6 comma 10 close bracket$ where $f$ fails to be continuous. Explain your answers.