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

question 191

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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $$f ( x ) = \sqrt { 58 - 3 x } , c = - 2 , \varepsilon = 0.2$$

• A) \(L = 8 ; \delta = 1.08\)
• B) \(L = 9 ; \delta = 1.05\)
• C) \(L = j - 7 ; \delta = 0.52\)
• D) \(\mathrm { L } = 8 ; \delta = 1.05\)

---

Definitions:

Percentage

A fraction or ratio expressed as a part of 100, used to denote proportion or comparison between quantities.

Missing Value

An absent data point or entry in a dataset, which may occur for various reasons and can impact the analysis if not properly handled.

Decimal Places

The number of digits to the right of the decimal point in a number, indicating precision.

Rate

The specified measured quantity of a thing in relation to a unit of another thing, often used in the context of interest, speed, or efficiency.