Provide an appropriate response.
-The definition of the limit, $\lim _ { x \rightarrow e } f ( x ) = L$ , means if given any number $\varepsilon > 0$ , there exists a number $\delta > 0$ , such that for all $x , 0 < | x - c | < \delta$ implies_____

Question

Provide an appropriate response. -The definition of the limit, $\lim _ { x \rightarrow e } f ( x ) = L$, means if given any number $\varepsilon > 0$, there exists a number $\delta > 0$, such that for all $x , 0 < | x - c | < \delta$ implies_____ A) $| f ( x ) - L | > \varepsilon$ B) $| f ( x ) - L | < \delta$ C) $| \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ D) $| f ( x ) - L | > \delta$

Quizplus · Accepted Answer

The definition is saying that if we choose any small positive number (epsilon), we can find a small positive distance (delta) around e such that if x is within that distance of e (but not equal to e), then the distance between f(x) and L will be less than epsilon. Therefore, the correct option is C.

Provide an Appropriate Response lim⁡x→ef(x)=L\lim _ { x \rightarrow e } f ( x ) = Llimx→e​f(x)=L

Provide an Appropriate Response $\lim _ { x \rightarrow e } f ( x ) = L$