Prove the Limit Statement
-Select the Correct Statement for the Definition

Multiple Choice

Prove the limit statement
-Select the correct statement for the definition of the limit: $\lim _ { x \rightarrow 0 } f ( x ) = L$ means that___________

A) if given any number $\varepsilon > 0$ , there exists a number $\delta > 0$ , such that for all $x$ , $0 < \left| x - x _ { 0 } \right| < \varepsilon$ implies $| f ( x ) - L | > \delta$ .
B) if given any number $\varepsilon > 0$ , there exists a number $\delta > 0$ , such that for all $x$ , $0 < \left| x - x _ { 0 } \right| < \varepsilon$ implies $| f ( x ) - L | < \delta$ .
C) if given a number $\varepsilon > 0$ , there exists a number $\delta > 0$ , such that for all $x$ , $0 < \left| x - x _ { 0 } \right| < \delta$ implies $| f ( x ) - L | > \varepsilon$ .
D) if given any number $\varepsilon > 0$ , there exists a number $\delta > 0$ , such that for all $x$ , $0 < \left| x - x _ { 0 } \right| < \delta$ implies $| f ( x ) - L | < \varepsilon$ .