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

question 146

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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $f ( x ) = - 3 x - 7 , L = - 19 , c = 4$ , and $\varepsilon = 0.01$

• A) \(\delta = 0.003333\)
• B) \(\delta = - 0.0025\)
• C) \(\delta = 0.001667\)
• D) \(\delta = 0.006667\)

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Definitions:

Long-run Equilibrium

A state in which all firms in a market are making zero economic profit, leading to an optimal allocation of resources.

Competitive Price-searcher

A market participant who sets prices through active search and strategy, often in markets with some degree of product differentiation.

Product Diversity

The variation of products and services offered in a market to meet different customer needs and preferences.

Firms Exit

This occurs when businesses cease operations and leave a market, typically due to factors like unprofitability, competitive pressures, or changing market conditions.