A Function $\mathrm { f } ( \mathrm { x } )$

question 93

Multiple Choice

A function $\mathrm { f } ( \mathrm { x } )$ , a point $\mathrm { c }$ , the limit of $\mathrm { f } ( \mathrm { x } )$ as $x$ approaches $\mathrm { c }$ , and a positive number $\varepsilon$ is given. Find a number $\delta > 0$ such that for all $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $$f ( x ) = 8 x - 9 , L = 15 , c = 3 \text {, and } \varepsilon = 0.01$$

• A) \(\delta = 0.0025\)
• B) \(\delta = 0.003333\)
• C) \(\delta = 0.000625\)
• D) \(\delta = 0.00125\)

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