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

question 152

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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $$f ( x ) = 7 x ^ { 2 } , L = 175 , c = 5 \text {, and } \varepsilon = 0.5$$

• A) \(\delta = 0.00715\)
• B) \(\delta = 0.00714\)
• C) \(\delta = 4.99285\)
• D) \(\delta = 5.00714\)

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Definitions:

Sample Means

The average value of a set of samples from a population.

Freshmen

First-year students at a high school, college, or university.

Simple Random Sample

A sample in which each member of the population has an equal chance of being selected, ensuring that the sample accurately reflects the population from which it is drawn.

Probability

The quantification of the probability of an event happening, represented by a numerical value ranging from 0 to 1.