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

Multiple Choice

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) $| f ( x ) - L | > \delta$