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

question 205

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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $f ( x ) = \sqrt { x + 2 } , L = 3 , c = 7$ , and $\varepsilon = 1$

• A) \(\delta = 16\)
• B) \(\delta = 4\)
• C) \(\delta = 5\)
• D) \(\delta = 7\)

---

Definitions:

Marketer

A marketer is a professional involved in the creation, communication, delivery, and exchange of offerings that have value for customers, clients, partners, and society at large.

Average Family Income

The mean amount of money earned by members of a family in a given period, often used to measure economic status.

Confidence Interval

A span of numbers obtained from sample observations, expected to encompass the value of an unseen population characteristic.

Null Hypothesis

A statement or hypothesis that indicates no statistical significance or effect, essentially asserting that any observed differences are due to chance.