Provide an Appropriate Response $L$ Is the Limit Of $f ( x )$

question 327

Multiple Choice

Provide an appropriate response.
-Identify the incorrect statements about limits.
I. The number $L$ is the limit of $f ( x )$ as $x$ approaches $c$ if $f ( x )$ gets closer to $L$ as $x$ approaches $x _ { 0 }$ .
II. The number $L$ is the limit of $f ( x )$ as $x$ approaches $c$ if, for any $\varepsilon > 0$ , there corresponds a $\delta > 0$ such that $\mid f ( x ) - L$ $\varepsilon$ whenever $0 < | x - c | < \delta$ .

III. The number $L$ is the limit of $f ( x )$ as $x$ approaches $c$ if, given any $\varepsilon > 0$ , there exists a value of $x$ for which $\mid f ( x )$ $\varepsilon .$

• A) I and III
• B) I and II
• C) I, II, and III
• D) II and III <

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