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

question 195

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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $\mathrm { f } ( \mathrm { x } ) = \sqrt { 17 - \mathrm { x } } , \mathrm { L } = 4 , \mathrm { c } = 1$ , and $\varepsilon = 1$

• A) \(\delta = - 9\)
• B) \(\delta = 8\)
• C) \(\delta = 12\)
• D) \(\delta = 7\)

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Definitions:

Efficacy

The ability to produce a desired or intended result, often used in the context of medications or treatments.

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Whether a therapeutic intervention works under real-world conditions.

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