Prove the Limit Statement
-Select the Correct Statement for the Definition

question 199

Multiple Choice

Prove the limit statement
-Select the correct statement for the definition of the limit: $\lim _ { x \rightarrow 0 } f ( x ) = L$ means that___________

• A) if given any number \(\varepsilon > 0\), there exists a number \(\delta > 0\), such that for all \(x\), \(0 < \left| x - x _ { 0 } \right| < \varepsilon\) implies \(| f ( x ) - L | > \delta\).
• B) if given any number \(\varepsilon > 0\), there exists a number \(\delta > 0\), such that for all \(x\), \(0 < \left| x - x _ { 0 } \right| < \varepsilon\) implies \(| f ( x ) - L | < \delta\).
• C) if given a number \(\varepsilon > 0\), there exists a number \(\delta > 0\), such that for all \(x\), \(0 < \left| x - x _ { 0 } \right| < \delta\) implies \(| f ( x ) - L | > \varepsilon\).
• D) if given any number \(\varepsilon > 0\), there exists a number \(\delta > 0\), such that for all \(x\), \(0 < \left| x - x _ { 0 } \right| < \delta\) implies \(| f ( x ) - L | < \varepsilon\).

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Definitions:

Attributable Interest

A financial term referring to the ownership interest or stake that a person or entity has in an investment, often influencing the share of profits or losses they would receive.

Consolidation

The process of combining the financial statements of two or more entities to form a single set of statements.

Financial Statements

Reports that provide an overview of a company's financial condition, including balance sheet, income statement, and cash flow statement.

Aggregation

The process of combining multiple items into a single group or total, often used in accounting and data analysis to simplify information.