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

question 188

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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } } , \mathrm { L } = \frac { 1 } { 2 } , \mathrm { c } = 2$ , and $\varepsilon = 0.3$

• A) \(\delta = 0.75\)
• B) \(\delta = 0.375\)
• C) \(\delta = 3\)
• D) \(\delta = 10\)

---

Definitions:

Dyadic Process

A two-way interaction or relationship where both parties influence each other's behavior.

Leader Interaction

The communication and relational dynamics between a leader and their team members or followers.

Subordinate

A subordinate is an individual who works under the direction of someone else, typically answering to a manager or supervisor in the organizational hierarchy.

Intra-Individual Level

Pertaining to processes or variations occurring within a single individual, as opposed to between individuals or in a group.