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) \(\delta = 10\)

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Definitions:

Debtor's Book Value

The value of all debts owed to a company, often reflecting the accounts receivable balance on the balance sheet.

Unsecured Creditors

Creditors who have lent money without taking any collateral, thus bearing a higher risk in case of debtor's default.

Liabilities With Priority

Obligations that are given preference over other liabilities in the case of liquidation or bankruptcy, often secured or legally mandated.

Liquidation

The process of closing down a business by selling its assets to pay off its debts, with any leftovers being distributed to shareholders.